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A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The Riemann problems used in the flux computation are determined using averaging kernels that extend over several computational cells. The usual CFL stability constraint is replaced with a constraint involving the kernel support size. This makes the method unconditionally stable with respect to the size of the computational cells, allowing the computational mesh to be refined locally to an arbitrary degree without altering solution stability. The practical implementation of the method is detailed for the shallow water equations with topographical source term. Computational examples report applications of the method to the linear advection, Burgers and shallow water equations. In the case of sharp bottom discontinuities, the need for improved, well‐balanced discretisations of the geometric source term is acknowledged. [ABSTRACT FROM AUTHOR]

Summary: Hybrid algorithms are an efficient and popular choice for computing the solutions of hyperbolic conservation laws. In general, hybrid algorithms involve low‐cost high‐order accurate schemes in smooth regions and non‐oscillatory shock‐capturing schemes in the vicinity of discontinuities. Troubled‐cell indicators which measure the smoothness of the solution play a significant role in the efficiency of hybrid algorithms. This article proposes a new troubled‐cell indicator utilising the smoothness indicators of WENO schemes for hyperbolic conservation laws. The proposed troubled‐cell indicators are simple, efficient, effective, and are used to construct three new adaptive WENO algorithms of high‐order accuracy. The hybrid algorithms developed are independent of the order and type of the WENO reconstruction. For demonstration, we have considered the fifth and seventh order WENO‐Z reconstruction. The first two algorithms have comparable accuracy and resolution of the solution across discontinuities to that of the WENO‐Z scheme but at a less computational cost. The third algorithm ensures the convergence of the proposed scheme to the correct entropy solution when applied to a hyperbolic conservation law with non‐convex flux for which the WENO schemes fail. We have performed several 1D and 2D numerical experiments to demonstrate the efficiency of the proposed algorithms and their performance compared with the WENO‐Z schemes. The proposed algorithms are efficient and take 30%–75% less computational time than the WENO‐Z schemes while retaining the advantages of WENO‐Z schemes. [ABSTRACT FROM AUTHOR]

This research study performs a numerical assessment of the inward solidification of phase change material (PCM) integrated with metal foam (MF) encapsulated in a horizontal cylindrical geometry. The cylinder is not at melting temperature at the beginning, and its outer surface is subjected to convection boundary conditions. The 1D phase change model is resolved by applying the temperature transforming technique using an in‐house computer program written in C++. Four different MF materials, aluminum, copper, nickel, and stainless steel, with various porosities, are used to examine the thermal behavior of the storage system. It is found that the use of copper as a MF with higher effective thermal conductivity remarkably enhances the elapsed time for complete solidification. Additionally, for a porosity value of 0.92, the time for total solidification of copper is diminished by 94%, while the complete solidification time for Stainless Steel is decreased by 65% in comparison to the situation where no MF is used. [ABSTRACT FROM AUTHOR]

Fluid flow in deformable fractures is important to many applications including hydraulic stimulation. Fracture flow simulations typically rely on the Poiseuille flow model which presumes laminar quasi‐steady‐state flow conditions with negligible inertia. The high flow rates involved in industrial applications bring these assumptions into question. The GG22 flow model is a new method to capture inertial effects and turbulent flow phenomena with a moderate increase in computational complexity. Here we develop and verify the first hydro‐mechanically coupled finite element – finite volume model for fracture flow which uses the GG22 model. We use the model to examine fracture flow between oscillating elastic plates and show that inertia may elicit phase‐shifts in the fluid response, larger fluid pressures and rock mass stresses, and induce wave‐like behaviour even in a quasi‐static rock mass. We then apply the model to hydraulic stimulation of a cemented fracture in both the viscous and toughness dominant propagation regimes and examine the influence of inertia and turbulence compared to Poiseuille flow. We demonstrate that inertial effects due to the variation of aperture are negligible in two‐dimensional KGD‐like fractures with constant injection rates. If the flow rates are large enough to invoke turbulent flow behaviour, then significantly different fracture propagation behaviour is observed. The modelling established in this article will serve as the basis to examine the role of inertia and turbulence in axisymmetrical radial fractures and dynamic stimulation with pressure pulsing where we expect the role of inertia to be more significant. [ABSTRACT FROM AUTHOR]

In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier–Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite‐volume methods for the Navier–Stokes equations, advection–diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier–Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf‐sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries. [ABSTRACT FROM AUTHOR]

Summary: This paper is dedicated to a numerical method based on a random choice as proposed in Glimm's scheme. It is applied to the problem of advection of a scalar quantity. The numerical scheme proposed here relies on a fractional step approach for which: the first step is performed using any classical finite‐volume scheme, and the second step is a cell‐wise update. This second step is a projection based on a random choice. The resulting scheme possesses a very low level of numerical diffusion. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh‐size. The algorithm performs very well on one‐dimensional and multi‐dimensional problems. This algorithm is very easy to implement even for multi‐processor computations. [ABSTRACT FROM AUTHOR]

Morphology‐adaptive multiphase models are becoming more established for the numerical description of complex gas‐liquid flows adapting dynamically to the local flow morphology. In the present study, two different numerical methods originally designed for distinct flow morphologies are combined, namely the volume‐of‐fluid and the Euler–Euler method. Both edge cases have been proven to be capable of delivering reliable predictions in the respective use cases. The long‐term goal is to improve the prediction of gas‐liquid flows, regardless of the flow regime in a specific application. To capture the system dynamics with a given grid resolution, the flow fields need to be predicted as precise as possible, while the shape of structures such as gas bubbles need to be recovered adequately in topology and shape. The goal is to obtain reliable predictions on intermediate mesh resolutions rather than relying on fine meshes requiring more computational resources. Therefore, a procedure is proposed to locally measure the degree of resolution. With this information, the hydrodynamics in the interface region can be controlled by means of a dedicated interfacial drag formulation in order to improve simulation results across several levels of spatial resolution. A modified formulation of buoyancy is proposed to prevent unphysical oscillations of vertical velocity near a horizontal interface. The functionality is demonstrated in a three‐dimensional case of a gas bubble rising in stagnant liquid and in a co‐current stratified air‐water channel flow in two‐dimensional space. The choice of these different applications demonstrates the general applicability of the proposed model framework. [ABSTRACT FROM AUTHOR]

In this work, inward solidification process of a spherical capsule subjected to a periodic boundary condition is numerically studied. The temperature transforming technique is utilized to solve the 1D phase change model and an in‐house model developed in C++. The interface position and the transient temperature profiles are evaluated with respect to the different oscillation amplitudes and oscillation frequencies of the periodically oscillating surface temperature. The results demonstrate that in the situation where the amplitude is 30, the elapsed time for total solidification is dropped by 23.7% compared to the case without oscillation. It is also found that there is a 21.8% reduction in the time for total solidification when the frequency is changed from ω = π/64 to ω = 0. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD) applies numerical methods to solve transport phenomena problems. These include, for example, problems related to fluid flow comprising the Navier–Stokes transport equations for either compressible or incompressible fluids, together with turbulence models and continuity equations for single and multi‐component (reacting and inert) systems. The design space is first segmented into discrete volume elements (meshing). The finite volume method, the subject of this article, discretizes the equations in time and space to produce a set of non‐linear algebraic expressions that are assigned to each volume element—cell. The system of equations is solved iteratively with algorithms like the semi‐implicit method for pressure‐linked equations (SIMPLE) and the pressure implicit splitting of operators (PISO). CFD is especially useful for testing multiple design elements because it is often faster and cheaper than experiments. The downside is that this numerical method is based on models that require validation to check their accuracy. According to a bibliometric analysis, the broad research domains in chemical engineering include: (1) dynamics and CFD‐DEM, (2) fluid flow, heat transfer, and turbulence, (3) mass transfer and combustion, (4) ventilation and the environment, and (5) design and optimization. Here, we review the basic theoretical concepts of CFD and illustrate how to set up a problem in the open‐source software OpenFOAM to isomerize n‐butane to i‐butane in a notched reactor under turbulent conditions. We simulated the problem with 1000, 4000, and 16 000 cells. According to the Richardson extrapolation, the simulation underestimates the adiabatic temperature rise by 7% with 16 000 cells. [ABSTRACT FROM AUTHOR]

In this study, we present a robust conservative time‐staggered scheme for variable density flow. This pressure correction scheme uses the compressible Navier–Stokes equations and is implemented in the collocated finite‐volume open‐source computational fluid dynamics solver code_saturne. The Helmholtz equation is solved for the pressure increment, taking the thermodynamic pressure into account and avoiding the acoustic time step limitation. The internal energy equation is used and completed by a source term derived from the discrete kinetic energy equation, thus enforcing total energy conservation and consistency for irregular solutions. A numerical analysis providing conditions ensuring the positivity of the thermodynamic variables is proposed. The scheme is verified and validated against analytical and experimental test cases. Its ability to reproduce the pressure variation while conserving the mass is demonstrated. Its conservative property and time convergence order are also verified. An irregular shock solution is studied, emphasizing the importance of the source term in the internal energy equation. Finally, the scheme is validated against reference numerical results on a two‐dimensional natural convection cavity and experimental data on a three‐dimensional ventilation test case. The comparison against experimental data is made using first‐and second‐order turbulent simulations. [ABSTRACT FROM AUTHOR]

The reduced dimension fracture flow model (referred to as the GG22 model) is a recently derived extension of the cubic law model for flow through fractures of variable aperture with fluid inertia effects. Novel numerical methods are required to solve the nonlinear partial differential equations governing the GG22 model, as it is more complex than the cubic law. The GG22 model is derived from Navier–Stokes, which allows the adoption of similar numerical methods to the Navier–Stokes equations, but the model contains its own idiosyncrasies which must be addressed. This article presents the first numerical methods to solve the GG22 model. An explicit multi‐step finite volume method is developed and verified. The method is based on deriving a Poisson equation for pressure with an additional continuity correction to overcome numerical instabilities. The critical timestep is derived and shown to be a function of the fundamental frequency of the fracture‐fluid system and the maximum fluid velocity. The results show excellent agreement with analytical solutions, and the method demonstrates a first‐order rate of fluid flux convergence in time and a second‐order rate of pressure convergence in space. The model is applied to a traveling aperture wave which shows that higher pressures are required to generate lower average fluxes than predicted by the cubic law. [ABSTRACT FROM AUTHOR]

During effusive volcanic crises, the eruption and propagation of lava flows pose a significant hazard to nearby populations, homes, and infrastructure. Consequently, timely lava flow forecasts are a critical need for volcano observatory and emergency management operations. Previous lava flow modeling tools are typically either too slow to produce timely forecasts, or are fast, but lack critical aspects of lava physics or important forecasting outputs. In particular, the strong thermal stratification present in laminar, high‐Prandtl number flows has generally been neglected. Bulk rheological changes have previously been computed from cell‐averaged temperatures, assuming that the flow is thermally mixed. Here, we detail the development and initial testing of Lava2d, a new two‐dimensional depth‐averaged finite volume model of lava flow propagation over natural terrain which accounts for bulk rheological changes due to thermorheological stratification. We use a novel approach to energy conservation based on tracking cooling and solidifying at the flow base and at the moving flow surface, allowing for the estimation of more realistic vertical thermorheological profiles, while maintaining computational efficiency, producing very timely model runs. We validate our approach with three examples: comparison with theoretical propagation of crust‐dominated lava flows, comparison with a large‐scale molten basalt experiment from the Syracuse University Lava Project, and efficiency testing and comparison with the initial phase of the 1984 Mauna Loa lava flows. Our model is shown to produce rapid, realistic forecasts, making it a good candidate for operationalization in active volcanic regions such as in Hawai'i. Plain Language Summary: During volcanic eruptions, lava flows pose a significant hazard to nearby populations, homes, and infrastructure. During lava flow crises, forecasts of lava flow advance, coverage, and arrival time can significantly help volcano observatories and emergency managers perform their operations. The most realistic forecasts are made from simulations of lava flows, which include a model of how lava flows cool and solidify as they travel. Although some models use realistic cooling, they are generally too slow to be used in emergencies. Most previous lava flow models have instead estimated this cooling by assuming that temperature within a lava flow does not vary significantly with depth; however, this assumption is not realistic. Real lavas are much cooler at the surface and base than in their cores. This difference has a large impact on the lava's overall speed. Here, we show the development of Lava2d, a new model of lava flow which directly incorporates these temperature differences. We test our model using theory, experiments, and comparison with a large natural lava flow, showing that our model produces realistic simulations very quickly. Key Points: Strong thermorheological stratification significantly impacts lava flow emplacement and coolingWe have developed a new depth‐averaged finite volume lava flow model (Lava2d) incorporating this stratificationThis model is capable of producing realistic inundation and advance rate forecasts on operational timescales [ABSTRACT FROM AUTHOR]

We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while maintaining high accuracy. We propose a new challenging test problem for shallow water codes, consisting of a steady circular hydraulic jump that can be physically unstable. We show that numerical methods are prone to either suppress the instability completely or form carbuncles. We test existing cures for the carbuncle. In our experiments, only the proposed method is able to avoid unphysical carbuncles without suppressing the physical instability. [ABSTRACT FROM AUTHOR]

This work is devoted to the numerical approximation of the shallow water Exner system. We investigate three different numerical strategies to discretize the Exner equation which expresses the evolution in time of the bed sediment. The numerical schemes are all based on the Lagrange‐projection formalism which consists in splitting the mathematical model into the acoustic and transport system. In particular, the Exner equation is taken into account either in the acoustic and transport steps, or only at the acoustic or transport level. The methods and their second‐order extensions are designed in such a way to satisfy the well‐balanced property, namely the "lake at rest" and the "constant bed slope" steady states. Numerical evidences are given to validate the numerical schemes. [ABSTRACT FROM AUTHOR]

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds‐averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open‐source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR‐F6 wing‐body‐nacelle‐pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times. [ABSTRACT FROM AUTHOR]

The Weighted Essentially Non‐Oscillatory (WENO) reconstruction provides higher‐order accurate solutions to hyperbolic conservation laws for convex flux. But it fails to capture composite structure in the case of non‐convex flux and converges to the wrong solution (Qiu & Shu SIAM J Sci Comput. 2008;31:584‐607). In this article, we have developed a Modified WENO (MWENO) scheme in the finite difference framework, which can resolve the composite structure and ensures the entropic convergence. The MWENO reconstruction procedure involves the identification of the troubled‐cells, followed by the use of first‐order monotone modification in the troubled‐cells and employ the fifth‐order WENO reconstruction in the non‐troubled cells. A new troubled‐cell indicator is developed using the information of the smoothness indicator of the WENO reconstruction. Numerical experiments are performed for 1D and 2D test cases, which ensure the entropic convergence of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this article, we consider the hyperbolic heat equation. This system is linear hyperbolic with stiff source terms and satisfies a diffusion limit. Some finite volume numerical schemes have been proposed which reproduce this diffusion limit. Here, we extend such schemes, originally defined on polygonal meshes, to conical meshes (using rational quadratic Bezier curves). We obtain really new schemes that do not reduce to the polygonal version when the conical edges tend to straight lines. Moreover, these schemes can handle curved unstructured meshes so that geometric error on initial data representation is reduced and geometry of the domain is improved. Extra flux coming from conical edge (through his midedge point) has a deep impact on the stabilization when compared with the original polygonal scheme. Cross‐stencil phenomenon of polygonal scheme has disappeared, and issue of positivity for the diffusion problem (although unresolved on distorted mesh and/or with varying cross‐section) has been in some sense improved. [ABSTRACT FROM AUTHOR]

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize‐then‐project' approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the ROM level). These are two main advantages compared to existing approaches. The fully discrete FOM is obtained by a finite volume discretization of the incompressible Navier‐Stokes equations on a collocated grid, with a forward Euler time discretization. Two variants of the time discretization method, the inconsistent and consistent flux method, have been investigated. The latter leads to divergence‐free velocity fields, also on the ROM level, whereas the velocity fields are only approximately divergence‐free in the former method. For both methods, accurate results have been obtained for test cases with different types of boundary conditions: a lid‐driven cavity and an open‐cavity (with an inlet and outlet). The ROM obtained with the consistent flux method, having divergence‐free velocity fields, is slightly more accurate but also slightly more expensive to solve compared to the inconsistent flux method. The speedup ratio of the ROM and FOM computation times is the highest for the open cavity test case with the inconsistent flux method. [ABSTRACT FROM AUTHOR]

Simulating fluid–structure interactions is important in many engineering applications. Navier–Stokes based models can accurately simulate free surface flows and efficiency is improved by transforming the equations into the sigma‐coordinate system in which the grid follows the free surface and bottom. This approach lacks the ability to simulate wave overturning and splashing, but it has been demonstrated to accurately simulate breaking waves. Incorporating structures in a free surface flow model is challenging. Many existing techniques require complex grids and cumbersome interpolation. The immersed boundary method avoids complicated grids by overlaying the object on the grid. Interpolation is still required at the object boundary, which may not conserve mass. It is also difficult to compute the force acting on the body. Conservation may be reclaimed by embedding the object into the mesh. However, this may result in small (cut) cells and numerical instability unless they are merged with neighboring cells. In this article, a new model is proposed and constructed using a modified sigma coordinate transformation. This limits the model to simulating objects that can be represented by upper and lower surfaces that are functions of x and y, but still allows for many simulations of engineering interest. In exchange for this compromise, several advantages are gained including: efficiency, mass conservation, and easy estimation of force. Model accuracy is demonstrated by comparing numerical predictions with analytical solutions and laboratory measurements for free surface flows interacting with a horizontal cylinder and NACA 0012 foil. [ABSTRACT FROM AUTHOR]

In this paper, we resolve the ever‐present confusion over the Quadratic Upwind Interpolation for Convective Kinematics (QUICK) scheme: it is a second‐order scheme or a third‐order scheme. The QUICK scheme, as proposed in the original reference (B. P. Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59‐98), is a third‐order (not second‐order) finite‐volume scheme for the integral form of a general nonlinear conservation law with point‐valued solutions stored at cell centers as numerical solutions. Third‐order accuracy is proved by a careful and detailed truncation error analysis and demonstrated by a series of thorough numerical tests. The QUICK scheme requires a careful spatial discretization of a time derivative to preserve third‐order accuracy for unsteady problems. Two techniques are discussed, including the QUICKEST scheme of Leonard. Discussions are given on how the QUICK scheme is mistakenly found to be second‐order accurate. This paper is intended to serve as a reference to clarify any confusion about third‐order accuracy of the QUICK scheme and also as the basis for clarifying economical high‐order unstructured‐grid schemes as we will discuss in a subsequent paper. [ABSTRACT FROM AUTHOR]

This article presents the development of a new inverse design algorithm capable of generating blade geometries for cavitating cascade flows. With this methodology, we demonstrate the controllability of the pressure distribution in and around the cavity and thereby provide a means to regulate the aggressiveness of blade cavitation phenomena. The solver proposed here uses the Tohoku–Ebara equation of state to model phase change, combined with bespoke preconditioning and multigrid methods designed to handle the system's ill conditioning and cope with the hypersonic flow regime of the mixture, respectively. Blade geometries and the cavitating flow field are calculated simultaneously in a robust and efficient manner, with a blade loading that matches the target distribution. In this article, the accuracy of the cavitating flow solver is first demonstrated for the NACA0015 hydrofoil case and associated experimental data. The inverse design procedure is then applied to a typical axial flow pump cascade: a new blade profile is generated with a topology that successfully reduces the gradient of the pressure jump at cavity closure. [ABSTRACT FROM AUTHOR]

This article is a rebuttal to the claim found in the literature that the monotonic upstream‐centered scheme for conservation laws (MUSCL) cannot be third‐order accurate for nonlinear conservation laws. We provide a rigorous proof for third‐order accuracy of the MUSCL scheme based on a careful and detailed truncation error analysis. Throughout the analysis, the distinction between the cell average and the point value will be strictly made for the numerical solution as well as for the target operator. It is shown that the average of the solutions reconstructed at a face by Van Leer's κ‐scheme recovers a cubic solution exactly with κ=1/3, the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term is already sufficiently small with a third‐order truncation error. Finally, noting that the target spatial operator is a cell‐averaged flux derivative, we prove that the leading truncation error of the MUSCL finite‐volume scheme is third‐order with κ=1/3. The importance of the diffusion scheme is also discussed: third‐order accuracy will be lost when the third‐order MUSLC scheme is used with an incompatible fourth‐order diffusion scheme for convection‐diffusion problems. Third‐order accuracy is verified by thorough numerical experiments for both steady and unsteady problems. This article is intended to serve as a reference to clarify confusions about third‐order accuracy of the MUSCL scheme, as a guide to correctly analyze and verify the MUSCL scheme for nonlinear equations, and eventually as the basis for clarifying high‐order unstructured‐grid schemes in a subsequent article. [ABSTRACT FROM AUTHOR]

The monodomain model is a widely used model in electrocardiology to simulate the propagation of electrical potential in the myocardium. In this paper, we investigate a positive nonlinear control volume finite element scheme, based on Godunov's flux approximation of the diffusion term, for the monodomain model coupled to a physiological ionic model (the Beeler–Reuter model) and using an anisotropic diffusion tensor. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in conforming finite element methods. The diffusion term which involves an anisotropic tensor is discretized on a dual mesh using the diffusion fluxes provided by the conforming finite element reconstruction on the primal mesh and the other terms are discretized by means of an upwind finite volume method on the dual mesh. The scheme ensures the validity of the discrete maximum principle without any restriction on the transmissibility coefficients. By using a compactness argument, we obtain the convergence of the discrete solution and as a consequence, we get the existence of a weak solution of the original model. Finally, we illustrate by numerical simulations that the proposed scheme successfully removes nonphysical oscillations in the propagation of the wavefront and maintains conduction velocity close to physiological values. [ABSTRACT FROM AUTHOR]

Summary: This works deals with sensitivity analysis (SA) for the Navier‐Stokes equations. The aim is to provide an estimate of the variance of the velocity field when some of the parameters are uncertain and then to use the variance to compute confidence intervals for the output of the model. First, we introduce the physical model and analyze its stability. The sensitivity equations are derived, and their stability analyzed as well. We propose a finite element‐volume numerical scheme for the state and the sensitivity, which is integrated into the open‐source industrial code TrioCFD. Finally, we present some numerical results: a steady and an unsteady test case for the channel flow problem are investigated. For the steady case, we compare the results to the Monte Carlo method and show how the SA technique succeeds in providing very accurate estimates of the variance. For the unsteady case, a new filtering procedure is proposed to deal with a sensitivity that grows in time. The filtered sensitivity is then used to compute the variance of the output and to provide confidence intervals. [ABSTRACT FROM AUTHOR]

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The energy collection element of a parabolic trough collector includes a selective coated metallic receiver tube inside an evacuated glass tube. Perpendicularly incident sun light on the parabolic trough mirror aperture is concentrated on the receiver tube highly nonuniformly along its circular direction. This solar energy is collected as thermal energy circulating a suitable heat transfer fluid (HTF) through the tube. This conjugate heat transfer phenomenon under nonuniform heat flux boundary condition is computationally studied applying 3D finite volume (FV) modelling technique of computational fluid dynamics coupled with Monte Carlo ray tracing (MCRT) optical data. The MCRT model simulates the actual flux profile around the receiver tube. Apart from a FV model, this coupled study requires expertise in, and access to, a suitable MCRT code. A combination of polynomial correlations and user‐defined function (UDF) is introduced in this article in order to minimize the need of MCRT codes from subsequent FV modelling of the receiver tube of the Luz Solar 2 (LS2) collector. The correlations are developed from a verified 3D MCRT model, which is equivalent to the local irradiation data as a function of receiver circular location. The UDF includes two algorithms: one to develop solar flux profile from the correlations around the receiver, and the other to calculate heat loss from the receiver. Interpreting the UDF into ANSYS Fluent, a 3D FV model of the LS2 receiver is developed and validated with experimental results. The effectiveness of the UDF as an alternative to MCRT code is verified. The FV model is capable to investigate the heat transfer characteristics of the LS2 collector receiver at different solar irradiation level, optical properties of the collector components, glass tube conditions, HTFs, inserts or swirl generators, collector length, and internal diameter of the tube. [ABSTRACT FROM AUTHOR]

The learning of Computer‐Aided Engineering (CAE) usually involves practical computer lessons on the use of CAE software. Software packages suitable for learning should be user‐friendly and accessible, with an affordable cost. However, the CAE freeware and proprietary software available in the market are relatively difficult to use for novices. Furthermore, most proprietary software packages are very costly, hindering the access of learners. In this study, a CAE freeware suite, CAE 3D, has been developed for supporting the learning of CAE technology. CAE 3D contains four modules for analyzing 3D solid mechanics, heat transfer, and mechanical vibration problems by the finite element method, and 3D fluid dynamics problems by the finite volume method. Unlike most CAE freeware applications, the user interface of CAE 3D is a purely graphical user interface instead of containing some text‐based user interfaces. As CAE 3D is user‐friendly and capable of analyzing various types of engineering problems, it is suitable for use as a learning tool of CAE. For example, learners can adjust parameters, such as geometry, material properties, and/or boundary conditions, to explore the effects of a given setting on the CAE results. This article explains the CAE learning process, development of CAE 3D software and application of CAE 3D to university classrooms. The classroom feedback indicates that the students were highly satisfied with CAE 3D in terms of the usability, the reliability of results and the contribution toward learning. These responses support the applicability of CAE 3D in CAE education. [ABSTRACT FROM AUTHOR]

Summary: The purpose of this work is to build a general framework to reconstruct the underlying fields within a finite volume (FV) scheme solving a hyperbolic system of PDEs (Partial Differential Equations). In an FV context, the data are piecewise constants per computational cell and the physical fields are reconstructed taking into account neighbor cell values. These reconstructions are further used to evaluate the physical states usually used to feed a Riemann solver which computes the associated numerical fluxes. The physical field reconstructions must obey some properties linked to the system of PDEs such as the positivity, but also some numerically based ones, like an essentially nonoscillatory behavior. Moreover, the reconstructions should be highly accurate for smooth flows and robust/stable for discontinuous solutions. To ensure a solution property preserving reconstruction, we introduce a methodology to blend high‐/low‐order polynomials and hyperbolic tangent reconstructions. A boundary variation diminishing algorithm is employed to select the best reconstruction in each cell. An a posteriori MOOD detection procedure is employed to ensure the positivity by recomputing the rare problematic cells using a robust first‐order FV scheme. We illustrate the performance of the proposed scheme via the numerical simulations for some benchmark tests which involve vacuum or near vacuum states, strong discontinuities, and also smooth flows. The proposed scheme maintains high accuracy on smooth profile, preserves the positivity and can eliminate the oscillations in the vicinity of discontinuities while maintaining sharper discontinuity with superior solution quality compared to classical highly accurate FV schemes. [ABSTRACT FROM AUTHOR]

Summary: Fluid injection–induced tensile opening is modeled using an extended finite volume method (XFVM). An embedded fracture strategy is used for the flow problem, that is, the fractures are discretized using finite volume segments without resolving the grid around them. Further, the discontinuities across fractures are modeled using special basis functions. The fracture openings due to enhanced fluid pressure and the associated shear slip due to traction free boundary condition on the fracture segments are both modeled using these special discontinuity basis functions. Mass transfer between fractures and matrix is modeled using the pressure difference. The enhancement of fracture storativity due to tensile opening leads to stronger coupling between flow and mechanics. An iterative scheme relying on the fixed‐stress approach for fractures, which conserves the stress dependent terms over each iteration of the flow problem, has been introduced. Tensile opening has been simulated for single fractures embedded in two‐ and three‐dimensional matrices. The convergence criterion for sequentially implicit fixed‐stress scheme for fractures embedded in elastic media is established and has been validated numerically. Further, for 2D simulations, the effect of the matrix permeability for fracture propagation due to tensile opening has been studied. [ABSTRACT FROM AUTHOR]

Summary: A fractured poroelastic body is considered where the opening of the fractures is governed by a nonpenetration law, whereas slip is described by a Coulomb‐type friction law. This physical model results in a nonlinear variational inequality problem. The variational inequality is rewritten as a complementary function, and a semismooth Newton method is used to solve the system of equations. For the discretization, we use a hybrid scheme where the displacements are given in terms of degrees of freedom per element, and an additional Lagrange multiplier representing the traction is added on the fracture faces. The novelty of our method comes from combining the Lagrange multiplier from the hybrid scheme with a finite volume discretization of the poroelastic Biot equation, which allows us to directly impose the inequality constraints on each subface. The convergence of the method is studied for several challenging geometries in 2D and 3D, showing that the convergence rates of the finite volume scheme do not deteriorate when it is coupled to the Lagrange multipliers. Our method is especially attractive for the poroelastic problem because it allows for a straightforward coupling between the matrix deformation, contact conditions, and fluid pressure. [ABSTRACT FROM AUTHOR]

In pseudopotential lattice Boltzmann (LB) models for simulating multicomponent flows, interaction forces between the components of a mixture lead to phase separation and interfacial tension. At the macroscopic scale, such LB models solve an advection‐diffusion equation for each component and the Navier‐Stokes equations for the fluid mixture. In this paper, the computational efficiency of the LB method is compared with a finite volume (FV) solver for the same macroscopic‐scale equations for a binary system in a two dimensional domain. The FV implementation replicates the phase separation of the LB model. Differences in the interfacial tension are due to truncation of the Taylor series expansion of the LB interaction force in the FV version. While the computations required to update the domain for each timestep can be completed faster with the FV approach, a smaller timestep is required to achieve stability, which negates the improvement in processing speed. The FV implementation, however, allows independent variation of model parameters, which is not possible in LB. For example, the viscosity can be changed without affecting interfacial tension or the extent of phase separation. Furthermore, it is possible to obtain low interfacial tensions without suppressing phase separation with the FV formulation. The significance of changing the diffusion rate of components on the deformation of a droplet in shear is also demonstrated. For three‐dimensional simulations, the finite volume approach is expected to be faster than LB and would benefit from the demonstrated flexibility in specifying model parameters. [ABSTRACT FROM AUTHOR]

Summary: This work is devoted to the numerical resolution in the multidimensional framework of a hierarchy of reduced models of the water wave equations, such as the Serre‐Green‐Naghdi model. A particular attention is paid to the dissipation of mechanical energy at the discrete level, which acts as a stability argument of the scheme, even with source terms such space and time variation of the bathymetry. In addition, the analysis leads to a natural way to deal with dry areas without leakage of energy. To illustrate the accuracy and the robustness of the strategy, several numerical experiments are carried out. In particular, the strategy is capable of treating dry areas without special treatment. [ABSTRACT FROM AUTHOR]

Natural convection in a triangular cavity filled with air is investigated numerically. In this paper, the cavity is exposed to air stream cooling exerted on its sides and it is heated by a fixed heat flux from the base. The air inside the cavity is assumed to be laminar and obeying Boussinesq approximation. The governing equations are solved numerically using the finite volume technique with SIMPLE algorithm. The results are achieved with a range of Rayleigh number (104 < Ra < 107), free stream Reynolds number (103 < Re∞ < 1.5 × 104), four aspect ratios (AR = 0.25, 0.5, 0.866, and 1) and five inclination angles (ϕ = 0°, 30°, 45°, 60°, 90°). The influence of these parameters is displayed on the stream function, isotherms lines, local and average Nusselt numbers. The results reveal that the heat transfer rate increases as Rayleigh number, free stream Reynolds number and AR increase. The highest heat transfer rate is obtained at ϕ = 0° while the lowest one is obtained at ϕ = 90°. Furthermore, as the AR augments, the local and average Nusselt numbers are enhanced and the stream function is formed of two symmetric counter‐rotating vortices. [ABSTRACT FROM AUTHOR]

A new global climate model setup using FESOM2.0 for the sea ice‐ocean component and ECHAM6.3 for the atmosphere and land surface has been developed. Replacing FESOM1.4 by FESOM2.0 promises a higher efficiency of the new climate setup compared to its predecessor. The new setup allows for long‐term climate integrations using a locally eddy‐resolving ocean. Here it is evaluated in terms of (1) the mean state and long‐term drift under preindustrial climate conditions, (2) the fidelity in simulating the historical warming, and (3) differences between coarse and eddy‐resolving ocean configurations. The results show that the realism of the new climate setup is overall within the range of existing models. In terms of oceanic temperatures, the historical warming signal is of smaller amplitude than the model drift in case of a relatively short spin‐up. However, it is argued that the strategy of "de‐drifting" climate runs after the short spin‐up, proposed by the HighResMIP protocol, allows one to isolate the warming signal. Moreover, the eddy‐permitting/resolving ocean setup shows notable improvements regarding the simulation of oceanic surface temperatures, in particular in the Southern Ocean. Key Points: A new climate model setup using an unstructured‐mesh ocean‐sea ice component has been developedMean state and long‐term drift under preindustrial climate conditions are evaluatedModeled climates using coarse and eddy‐resolving ocean configurations are compared [ABSTRACT FROM AUTHOR]

Summary: Using a hybrid Lagrangian‐Eulerian approach, a level set function–based immersed interface method (LS‐IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS‐IIM involves finite volume method for the fluid solver, Galerkin finite element method for the structural solver, and a block‐iterative partitioned method–based fully implicit coupling between the two solvers. The novelty of the proposed method is a level set function–based direct implementation of fluid‐solid interface boundary conditions in both the solvers. Another novelty is the computation of the level set function from a geometric method instead of differential equations commonly used in level set methods—the novel geometric as compared to the traditional method is found to be more accurate and less time‐consuming. The LS‐IIM is demonstrated as second‐order accurate. Verification study is presented first separately for both the solvers and then together for four fluid‐structure interaction (FSI) problems, with different levels of complexity including lid‐driven flow, channel flow, and free‐stream flow. Benchmark solutions are presented for two class of FSI problems: first, easy to set up and less time‐consuming and, second, a reasonably challenging and complex FSI problem involving sharp edges and forced‐motion of the flexible structure. The benchmark solutions are proposed at steady state for the first problem, after a verification study with two open‐source solvers and, at periodic state, after a validation with published experimental results for the second problem. Our benchmark solutions may be useful for verification study in future. [ABSTRACT FROM AUTHOR]

Summary: This article deals with fast transient phenomena involving fluids and structures undergoing large displacements and rotations, associated with nonlinear local behavior, such as plasticity, damage, and failure. A new approach is proposed to handle the interaction between a structure and the compressible fluid it is immersed into. The equations governing the evolution of the structure and the fluid are discretized using Lagrangian shell finite‐elements and Eulerian cell‐centered finite volume approaches, respectively. The meshes of the structure and the fluid are totally independent from one another and fully unstructured. The proposed method uses an intermediate body through which the physical quantities are exchanged between the fluid and the structure. It relies on the solution of local one‐dimensional fluid‐structure Riemann problems in local frames related to the normal of the structure. Since the proposed approach does not require to subdivide the fluid cell according to the structure geometry, it can deal with complex nonmanifold thin structures. Nevertheless, it is shown through some numerical experiments that, thanks to some features described in this article, the method provides accurate results. It is also shown that the method can cope with large 3D problems. [ABSTRACT FROM AUTHOR]

Summary: Intrusive reduced order modeling techniques require access to the solver's discretization and solution algorithm, which are not available for most computational fluid dynamics codes. Therefore, a nonintrusive reduction method that identifies the system matrix of linear fluid dynamical problems with a least‐squares technique is presented. The methodology is applied to the linear scalar transport convection‐diffusion equation for a 2D square cavity problem with a heated lid. The (time‐dependent) boundary conditions are enforced in the obtained reduced order model (ROM) with a penalty method. The results are compared and the accuracy of the ROMs is assessed against the full order solutions and it is shown that the ROM can be used for sensitivity analysis by controlling the nonhomogeneous Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

Summary: The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver that is known to be plagued by various forms of numerical shock instability. In this paper, we clarify that the shock instability exhibited by this scheme is primarily triggered by the spurious activation of the antidiffusive terms present in the first and third Riemann flux components on the transverse interfaces adjoining the shock front due to numerical perturbations. These erroneously activated terms are shown to counteract the favorable damping mechanism provided by its inherent HLL‐type diffusive terms, causing an unphysical variation of the conserved quantity ρu both along and across the numerical shock. To prevent this, two distinct strategies are proposed termed as Selective Wave Modification and Anti Diffusion Control. The former focuses on enhancing the quantity of the favorable HLL‐type dissipation available on these critical flux components by carefully increasing the magnitudes of certain nonlinear wave speed estimates, while the latter focuses on directly controlling the magnitude of these critical antidiffusive terms. A linear perturbation analysis is performed to gauge the effectiveness of these cures and to estimate a von Neumann–type stability bounds on the CFL number associated with their use. Results from a variety of classic shock instability test cases show that the proposed strategies are able to provide excellent shock stable solutions even on grids that are highly elongated across the shock front without compromising the accuracy on inviscid contact or shear dominated viscous flows. Numerical shock instability in the HLLEM scheme is found to be triggered by the erroneous activation of certain antidiffusive terms, within the numerical shock region, which counteract the stabilizing action of the inherent HLL‐type diffusive terms. Two distinct strategies named 'Selective Wave Modification' and 'Anti Diffusion Control' are proposed to avert the instability. The schemes resulting from these, are found to be robust on a wide variety of problems involving a wide range of grid aspect ratios. [ABSTRACT FROM AUTHOR]

This paper presents a two‐dimensional shallow water equations code coupled with a physically based erosion model, able to predict the opening and evolution of breaches forming in levees built with either cohesive or noncohesive material. The bottom elevation change is evaluated using an excess shear‐stress equation, which accounts for the hydrodynamic conditions and for the material characteristics. The proposed model modifies the local topography at runtime wherever the levee is overtopped without having to predefine the position and shape of the breach. The model is implemented in CUDA programming language, so that simulations can be run on graphics processing units, guaranteeing fast execution times even for high‐resolution meshes and large domains. The validation is performed based on several experimental tests, and numerical predictions are in good agreement with the measurements. The strengths and weaknesses of the proposed approach are also discussed by comparison with a sediment transport model based on the Exner equation: While the latter gives good results only for breaches forming in levees built with noncohesive material, the proposed model can also be applied to cohesive embankments. The application to a historical flood event is also presented, showing that the model can effectively be employed for real field simulations also in the case of multiple breaches. Key Points: The paper presents a 2D SWE model able to simulate the opening of a levee breach due to overtopping and the subsequent floodingThe physically based erosion model allows predicting the breach evolution in levees made of cohesive or noncohesive materialThe model can be applied to real cases, thanks to the fast execution times guaranteed by the GPU parallelization of computations [ABSTRACT FROM AUTHOR]

Summary: This paper describes the implementation of a numerical solver that is capable of simulating compressible flows of nonideal single‐phase fluids. The proposed method can be applied to arbitrary equations of state and is suitable for all Mach numbers. The pressure‐based solver uses the operator‐splitting technique and is based on the PISO/SIMPLE algorithm: the density, velocity, and temperature fields are predicted by solving the linearized versions of the balance equations using the convective fluxes from the previous iteration or time step. The overall mass continuity is ensured by solving the pressure equation derived from the continuity equation, the momentum equation, and the equation of state. Nonphysical oscillations of the numerical solution near discontinuities are damped using the Kurganov‐Tadmor/Kurganov‐Noelle‐Petrova (KT/KNP) scheme for convective fluxes. The solver was validated using different test cases, where analytical and/or numerical solutions are present or can be derived: (1) A convergent‐divergent nozzle with three different operating conditions; (2) the Riemann problem for the Peng‐Robinson equation of state; (3) the Riemann problem for the covolume equation of state; (4) the development of a laminar velocity profile in a circular pipe (also known as Poiseuille flow); (5) a laminar flow over a circular cylinder; (6) a subsonic flow over a backward‐facing step at low Reynolds numbers; (7) a transonic flow over the RAE 2822 airfoil; and (8) a supersonic flow around a blunt cylinder‐flare model. The spatial approximation order of the scheme is second order. The mesh convergence of the numerical solution was achieved for all cases. The accuracy order for highly compressible flows with discontinuities is close to first order and, for incompressible viscous flows, it is close to second order. The proposed solver is named rhoPimpleCentralFoam and is implemented in the open‐source CFD library OpenFOAM®. For high speed flows, it shows a similar behavior as the KT/KNP schemes (implemented as rhoCentralFoam‐solver, Int. J. Numer. Meth. Fluids 2010), and for flows with small Mach numbers, it behaves like solvers that are based on the PISO/SIMPLE algorithm. [ABSTRACT FROM AUTHOR]

Summary: The flux‐vector splitting scheme of Steger and Warming is a popular approach for the Euler equations. In this work, we consider the spectrum of the scheme and show for 1≤γ≤5/3, where γ is the ideal gas constant, that the eigenvalues are strictly real and of an appropriate sign. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of surface texturing in a partial pad journal bearing through a series of controlled experiments at operating conditions, promoting mixed or boundary regimes of lubrication. Improvements to load carrying capacity are observed under certain operating conditions. A comprehensive computational finite volume multiphase fluid dynamics analysis, including vapour transport equation and modified finite-size cavity Rayleigh-Plesset model, is used to study the effect of indented surface textures in the microscale contact domain and within the individual textures themselves. The results show improved conditions with a textured journal through promotion of micro-hydrodynamic effect, delaying the effect of lubricant rupture, thus extending the effective load bearing region. A very good agreement is obtained between measurements and predictions. [ABSTRACT FROM AUTHOR]

Summary: Determining boundary conditions (BCs) for incompressible flows is such a delicate matter that affects the accuracy of the results. In this research, a new characteristic‐based BC for incompressible Navier‐Stokes equations is introduced. Discretization of equations has been done via finite volume. Additionally, artificial compressibility correction has been employed to deal with equations. Ordinary extrapolation from inner cells of a domain was used as a traditional way to estimate pressure and velocities on solid wall and inlet/outlet boundaries. Here, this method was substituted by the newly proposed BCs based on the characteristics of artificial compressibility equations. To follow this purpose, a computer code has been developed to carry out series of numerical tests for a flow over a backward‐facing step and was applied to a wide range of Reynolds numbers and grid combinations. Calculation of convective and viscous fluxes was done using Jameson's averaging scheme. Employing the characteristic‐based method for determining BCs has shown an improved convergence rate and reduced calculation time comparing with those of traditional ones. Furthermore, with the reduction of domain and computational cells, a similar accuracy was achieved for the results in comparison with the ones obtained from the traditional extrapolation method, and these results were in good agreement with the ones in the literature. [ABSTRACT FROM AUTHOR]

Summary: The goal of this paper is to show the effectiveness of a newly developed estimate of the truncation error calculated based on C1 interpolation of the solution weighted by the adjoint solution as the adaptation indicator for an unstructured finite volume solver. We will show that adjoint‐based mesh adaptation based on the corrected functional using the new developed truncation error estimate is capable of adapting the mesh to improve the accuracy of the functional and the convergence rate. Both discrete and continuous adjoint solutions are used for adaptation. Results are significantly better with new truncation error estimate than with previously used estimates. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a central essentially non‐oscillatory approximation based on a quadratic polynomial reconstruction is considered for solving the unsteady 2D Euler equations. The scheme is third‐order accurate on irregular unstructured meshes. The paper concentrates on a method for a metric‐based goal‐oriented mesh adaptation. For this purpose, an a priori error analysis for this central essentially non‐oscillatory scheme is proposed. It allows us to get an estimate depending on the polynomial reconstruction error. As a third‐order error is not naturally expressed in terms of a metric, we propose a least‐square method to approach a third‐order error by a quadratic term. Then an optimization problem for the best mesh metric is obtained and analytically solved. The resulting mesh optimality system is discretized and solved using a global unsteady fixed‐point algorithm. The method is applied to an acoustic propagation benchmark. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model to predict flow-induced shear failure along pre-existing fractures is presented. The framework is based on a discrete fracture representation embedded in a continuum describing the damaged matrix. A finite volume method is used to compute both flow and mechanical equilibrium, whereas specifically tailored basis functions are used to account for the physics at discontinuities. The failure criterion is based on a maximum shear strength limit, which changes with varying compressive stress on the fracture manifold. The displacements along fracture manifolds are obtained such that force balance is achieved under conditions, where shear stress of the failing fracture segment is constrained to the maximum shear strength at the segment. Simultaneously, the fluid pressure is computed independently of the shear slip. A relaxation model approach is used to obtain the maximum shear limit on the fracture manifold, which leads to grid convergence. [ABSTRACT FROM AUTHOR]

The Lagrangian approach is usually used for the simulation of flow with strong shock waves. Moreover, this approach is particularly well suited to treatment of material interfaces in the case of multimaterial flows.Unfortunately, this formulation leads to very large deformations in the mesh. The arbitrary Lagrangian-Eulerian method overcomes this drawback by using a mesh regularization that is based on an analysis of cell geometry. The regularization step may be considered as a method used to correct the nonconvex and potentially tangled cells that constitute the mesh. In this paper, we present a new approach to mesh regularization. Instead of using a purely geometric criterion, we propose that the mesh evolution is computed on the basis of the flow vorticity. This approach is called the large Eddy limitation method, and it is aimed here to be used in finite volume direct arbitrary Lagrangian-Eulerian methods. The large Eddy limitation method is general, which means that it is not restricted to applications in the finite volume framework dedicated to fluid flow simulation; for instance, it could also be naturally applied to the finite element framework. [ABSTRACT FROM AUTHOR]

The idea of hp-adaptation, which has originally been developed for compact schemes (such as finite element methods), suggests an adaptation scheme using a mixture of mesh refinement and order enrichment based on the smoothness of the solution to obtain an accurate solution efficiently. In this paper, we develop an hp-adaptation framework for unstructured finite volume methods using residual-based and adjoint-based error indicators. For the residual-based error indicator, we use a higher-order discrete operator to estimate the truncation error, whereas this estimate is weighted by the solution of the discrete adjoint problem for an output of interest to form the adaptation indicator for adjoint-based adaptations. We perform our adaptation by local subdivision of cells with nonconforming interfaces allowed and local reconstruction of higher-order polynomials for solution approximations. We present our results for two-dimensional compressible flow problems including subsonic inviscid, transonic inviscid, and subsonic laminar flow around the NACA 0012 airfoil and also turbulent flow over a flat plate. Our numerical results suggest the efficiency and accuracy advantages of adjoint-based hp-adaptations over uniform refinement and also over residual-based adaptation for flows with and without singularities. [ABSTRACT FROM AUTHOR]

Parallel domain decomposition methods are natural and efficient for solving the implicity schemes of diffusion equations on massive parallel computer systems. A finite volume scheme preserving positivity is essential for getting accurate numerical solutions of diffusion equations and ensuring the numerical solutions with physical meaning. We call their combination as a parallel finite volume scheme preserving positivity, and construct such a scheme for diffusion equation on distorted meshes. The basic procedure of constructing the parallel finite volume scheme is based on the domain decomposition method with the prediction-correction technique at the interface of subdomains: First, we predict the values on each inner interface of subdomains partitioned by the domain decomposition. Second, we compute the values in each subdomain using a finite volume scheme preserving positivity. Third, we correct the values on each inner interface using the finite volume scheme preserving positivity. The resulting scheme has intrinsic parallelism, and needs only local communication among neighboring processors. Numerical results are presented to show the performance of our schemes, such as accuracy, stability, positivity, and parallel speedup. [ABSTRACT FROM AUTHOR]

A novel numerical scheme for slug capturing in pipes using a 1-dimensional transient hyperbolic 5-equation 2-fluid model is presented. Previous work has shown that 1-dimensional 2-fluid models are able to capture slug flow automatically. In this work, a similar approach is further developed using a new numerical scheme, applied to a hyperbolic 5-equation 2-fluid model. Starting from a finite volume discretisation of a 5-equation 2-fluid hyperbolic model and adding appropriate closure relations, a second-order code is implemented and applied to air-water flows in horizontal pipes, simulating the 2-phase to 1-phase flow process. The code is evaluated in some common standard test cases. A slug capturing application is also discussed. We show, in an air/water horizontal pipe, slug initiation, growth, and development. Moreover, a grid refinement analysis is performed showing that the method is grid independent and we show the code capability to take into account eventual surface tension effects, through the instantaneous pressure relaxation process. Finally, a prediction of flow regime transitions is shown and compared with a well-known theoretical flow pattern map in addition to a preliminary comparison of computed slug characteristics against well-known empirical correlations. [ABSTRACT FROM AUTHOR]