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In this paper, numerical study on natural convection heat transfer for confined thermodependent power-law fluids is conducted. The geometry of interest is a fluid-filled square enclosure where a uniform flux heating element embedded on its lower wall is cooled from the vertical walls while the remaining parts of the cavity are insulated, without slipping conditions at all the solid boundaries. The governing partial differential equations written in terms of non-dimensional velocities, pressure and temperature formulation with the corresponding boundary conditions are discretized using a finite volume method in a staggered grid system. Coupled equations of conservation are solved through iterative Semi Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The effects of pertinent parameters, which are Rayleigh number (103 = Ra = 106), power-law index (0.6 = n = 1.4), Pearson number (0 = m = 20) and length of the heat source (0.2 = W = 0.8) on the cooling performance are investigated. The results indicate that the cooling performance of the enclosure is improved with increasing Pearson and Rayleigh numbers as well as with decreasing power-law index and heat source length. [ABSTRACT FROM AUTHOR]

This paper presents a new sub-grid flood inundation model aimed at high computational performance. The model solves the two-dimensional shallow water equations (SWE) by a Godunov-type finite volume (FV) method that uses two nested meshes. Runtime computations are performed at a coarse computational mesh, while a fine mesh is used to incorporate fine resolution information into the solution at pre-processing level. New upscaling methods are separately derived for each of the terms in the SWE based on the integration of the governing equations over subdomains defined by the coarse resolution grid cells. The accuracy and performance of the model are tested through artificial and real-world test problems. Results showed that (i) for the same computational (coarse mesh) resolution, the inclusion of sub-grid information delivers more accurate results than a single-mesh FV model and (ii) for the same accuracy and at low resolution, the proposed methods improve computational performance. [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]

This paper aims to present a numerical study of dam break flow in the presence of an obstacle. A model based on the modified Non-Linear Shallow Water Equations with cross section and a dispersive treatment was solved numerically using a momentum-conservative finite volume method on a staggered grid. To validate the numerical model, several benchmark tests were carried out. Comparison of the computed results with the analytical and experimental data shows that the numerical model here proposed the flow with high accuracy. Moreover, the effect of the obstacle’s dimensions on the water height was examined. The extension to different contraction geometries of the simulation channel was examined.

An alternative cell-vertex entropy-stable finite volume method for the system of Euler equations is presented. It is derived from the residual distribution method, using the signals from each triangular element as a foundation for controlling entropy. Each signal has an entropy-conserved and entropy-stable components. From a median-dual area perspective, these signals can be interpreted as a line integral of the fluxes along the control volume boundaries of the cell-vertex approach. The new method includes a first-order version which is positive together with a linearity-preserving second order approach. A second order limited version is also presented using entropy as the guiding principle for limiting. Results herein demonstrate that the new method is more accurate and robust relative to the current cell-vertex entropy-stable finite volume method. [ABSTRACT FROM AUTHOR]

In this work, an implicit finite-volume-element (FVE) method is extended to efficiently simulate the vortical structure of unsteady turbulent flows in domains with moving meshes. The arbitrary Lagrangian-Eulerian (ALE) approach is used to consider the motion of a hybrid mesh distributed in the solution domain. Conventional turbulence models are applied to simply confirm the sample achieved efficiency and accuracy in solving complex turbulent flow domains with moving boundaries. In this regard, the advective terms in the Navier-Stokes equations, including those in the transport equations for the applied turbulence models, are treated in a rather innovative manner. In other words, an advanced physical influence scheme (PIS) is suitably introduced in the context of extended ALE formulations. The accuracy and efficiency of the extended method are carefully evaluated by simulating various turbulent flows, including the fluid flow in stationary domains, separated turbulent flow over a bluff body problem, and the dynamic stall of fluid flow over a flapping airfoil. Comparing the current solutions with experimental data, it is shown that the current PIS-ALE method provides better accuracy and efficiency than those of past numerical methods, which used similar turbulence models in their algorithms. [ABSTRACT FROM AUTHOR]

Anisotropic materials are those that the value of a property depends on the direction of analysis. This article addresses both analytical and numerical stress computation for orthotropic beams under normal and shear loads. The analytical solution is based on potential polynomial functions and the present work establishes general strategies which allow systematic evaluation of the polynomial coefficients. The numerical approximation uses an alternative formulation of finite volumes based on an area weighted average associated with parabolic interpolation functions. The numerical scheme is verified against results obtained for orthotropic beams using both the analytical method and a classical finite volume approximation. Assessment of the global error based on the L 2 norm indicates a high convergence rate and substantially smaller absolute differences when compared to the conventional finite volume approximation. [ABSTRACT FROM AUTHOR]

When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume (FV) schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. In this paper, we propose a rotated characteristic decomposition technique which requires only one-time decomposition for multi-dimensional reconstructions. The rotated direction depends only on the gradient of a specific physical quantity which is cheap to calculate. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume (WENO-FV) scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

• New least-squares based finite volume (FV) scheme for diffusion equation. • Novel gradient scheme with only cell-centered unknowns and compact neighbourhood stencil. • Consistent treatment of normal fluxes in diffusion equation and gradient reconstruction. • Discontinuities in diffusion coefficient and tangential flux can be handled. • FV scheme estimates solution and fluxes to second and first order accuracy respectively on arbitrary polygonal meshes. We propose a new second-order accurate finite volume (FV) scheme for diffusion equations with discontinuous coefficients on unstructured meshes. This scheme is based on a novel least squares reconstruction with a compact neighbourhood that computes the cell-centered diffusion fluxes from the normal diffusion flux at cell faces. We propose two variants of the scheme rooted in the concept of "alpha damping" (AD), which are both linearly exact on arbitrary mesh topologies even when the tangential diffusive fluxes are discontinuous. The first variant, referred to as AD-G (Alpha Damping-Gradient), effects the discretisation of the normal derivative while the second, referred to as AD-F (Alpha Damping-Flux), involves discretisation of the normal fluxes. It is shown that harmonic averaging for diffusion coefficient at the faces is essential for the accuracy of the solution with the AD-G scheme but this condition is not necessary for the AD-F scheme. Numerical experiments demonstrate that the proposed FV schemes estimate the solution and fluxes to second and first order accuracy respectively for discontinuous diffusion problems on generic polygonal meshes. Studies also show that these schemes are discrete extremum preserving (DEP) and can be implemented with relative ease for diffusion problems in existing legacy codes. [ABSTRACT FROM AUTHOR]

The purpose of this study concerns the establishment of three-dimensional numerical simulation of the coupling between fluid flow and internal erosion within a porous medium. In order to properly investigate suffusion process in porous media, we present a finite volumes method using explicit scheme for solving advection–dispersion–deposition equation on three-dimensional grids. The accuracy and the robustness of the proposed finite volume method are assessed by means of various numerical test cases and validated by the adjustment of experimental results. [ABSTRACT FROM AUTHOR]

Euler equations with a gravitational source term (PDEs) admit a hydrostatic equilibrium state where the source term exactly balances the flux gradient. The property of exact preservation of the equilibria is highly desirable when the PDEs are numerically solved. Li and Xing (J Comput Phys 316:145–163, 2016) proposed a high-order well-balanced characteristic-wise finite volume weighted essentially non-oscillatory (FV-WENO) scheme for the cases of isothermal equilibrium and polytropic equilibrium. On the contrary to what was claimed, the scheme is not well-balanced. The root of the problem is the precarious effects of a non-zero sensitivity parameter in the nonlinear weights of the WENO polynomial reconstruction procedure (WENO operator). The effects are identified in the theoretical proof for the well-balanced scheme and verified numerically on a coarse mesh resolution and a long time simulation of the PDEs. In this study, two simple yet effective numerical techniques derived from the multiplicative-invariance (MI) property of a WENO operator are invoked to rectify the sensitivity parameter’s dependency yielding a correct proof for the sensitivity parameter-independent (characteristic-wise) well-balanced FV-WENO scheme. The (non-)well-balanced nature of the schemes is demonstrated with several one- and two-dimensional benchmark steady state problems and a small perturbation over the steady state problems. Moreover, the one-dimensional Sod problem under the gravitational field is also simulated for showing the performance of the well-balanced FV-WENO scheme in capturing shock, contact discontinuity, and rarefaction wave in an essentially non-oscillatory nature. It also indicates that the numerical scheme with the third-order Runge–Kutta time-stepping scheme should take the CFL number less than 0.5 to mitigate the Gibbs oscillations at the shock without increasing the numerical dissipation artificially in the Lax–Friedrichs numerical flux. [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 unstructured finite volume method, loop on different mesh components such as cells, faces, nodes, etc is used widely for the traversal of data. Mesh loop results in direct or indirect data access that affects data locality significantly. By loop on mesh, many threads accessing the same data lead to data dependence. Both data locality and data dependence play an important part in the performance of GPU simulations. For optimizing a GPU-accelerated unstructured finite volume Computational Fluid Dynamics (CFD) program, the performance of hot spots under different loops on cells, faces, and nodes is evaluated on Nvidia Tesla V100 and K80. Numerical tests under different mesh scales show that the effects of mesh loop modes are different on data locality and data dependence. Specifically, face loop makes the best data locality, so long as access to face data exists in kernels. Cell loop brings the smallest overheads due to non-coalescing data access, when both cell and node data are used in computing without face data. Cell loop owns the best performance in the condition that only indirect access of cell data exists in kernels. Atomic operations reduced the performance of kernels largely in K80, which is not obvious on V100. With the suitable mesh loop mode in all kernels, the overall performance of GPU simulations can be increased by 15%-20%. Finally, the program on a single GPU V100 can achieve maximum 21.7 and average 14.1 speed up compared with 28 MPI tasks on two Intel CPUs Xeon Gold 6132. [ABSTRACT FROM AUTHOR]

The stability of the high-order finite volume method for hyperbolic systems is based on non-linear procedures that prevent the creation of non-physical oscillations. Traditional techniques use the a priori paradigm where the procedure is carried out with the current time step solution. The a posteriori paradigm lies on an advanced in time candidate solution and a posterior evaluation of its stability, followed by a cure when necessary. To compare the two strategies, we propose a detailed study using the non-conservative shallow-water equations as a prototype, where both techniques are applied together in the framework of second-order linear reconstruction for the sake of simplicity. Then, a hybrid version combining the most positive aspects of both methods is proposed and analysed. [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]

The technological advancements of the last few decades have fostered the use of two-dimensional (2D) Shallow water Equations (SWE) flood simulations not only in academic research but also in practical real-world applications and territorial planning. The evaluation of flow resistance due to friction is crucial as it plays a relevant role in a variety of flow conditions. However, problems arise in dam-break and overland flow applications involving very small water depth because the time scale connected to the friction term may be much smaller than the hydrodynamic time scale. To cope with this issue, known as source term stiffness, an implicit treatment of the friction term is frequently adopted in Finite Volume (FV) numerical schemes, but there are cases (null roughness coefficient or null flow velocity) where a division by zero may occur during calculations, leading to a crash of the algorithm. Herein, we propose a reformulation of the implicit friction term that is general, more stable and computationally efficient (with a speed-up of approximately 3 times for the routine running the friction computation) than currently available approaches. The novel implicit method allows to manage special conditions with null roughness or null discharge, without resorting to ad-hoc thresholds, and can be easily implemented in existing schemes with pointwise friction treatment. The novel friction approach is implemented in a purposely simple FV numerical scheme (hydrostatic reconstruction to account for the bed slope terms, first-order accuracy in time and space) - to better focus on the friction term treatment - and it is validated against analytical, synthetic, laboratory and real-world case studies, showing promising capabilities. [ABSTRACT FROM AUTHOR]

This article provides the high-order finite difference and finite volume ghost multi-resolution weighted essentially non-oscillatory (GMR-WENO) schemes for solving hyperbolic conservation laws on structured meshes. We only utilize the information defined on one big central spatial stencil without introducing any equivalent multi-resolution representations. These GMR-WENO schemes utilize orthogonal Legendre basis to construct high degree polynomials of big central spatial stencils and use a L 2 projection methodology to obtain a series of ghost low degree polynomials whose degree could gradually range from the highest degree to the zeroth degree. Each of these GMR-WENO schemes only utilizes one big central spatial stencil to achieve arbitrary high-order accuracy in smooth regions and could gradually reduce to the first-order accuracy nearby strong discontinuities. The linear weights of such GMR-WENO schemes can be any positive numbers with a summation of one. This is the first time that only one central spatial stencil is utilized in designing high-order finite difference and finite volume WENO schemes. These GMR-WENO schemes have a simple construction and can easily achieve arbitrary high-order accuracy in higher dimensions. Benchmark examples are provided to demonstrate the efficiency of these GMR-WENO schemes. [ABSTRACT FROM AUTHOR]

Efficient modeling of flow physics is a prerequisite for a reliable computation of free-surface environmental flows. Non-hydrostatic flows are often present in shallow water environments, making the task challenging. In this work, we use the method of weighted residuals for modeling non-hydrostatic free surface flows in a depth-averaged framework. In particular, we focus on the Vertically Averaged and Moment (VAM) equations model. First, a new derivation of the model is presented using expansions of the field variables in sigma-coordinates with Legendre polynomials basis. Second, an efficient two-step numerical scheme is proposed: the first step corresponds to solving the hyperbolic part with a second-order path-conservative PVM scheme. Then, in a second step, non-hydrostatic terms are corrected by solving a linear Poisson-like system using an iterative method, thereby resulting in an accurate and efficient algorithm. The computational effort is similar to the one required for the well-known Serre-Green-Naghdi (SGN) system, while the results are largely improved. Finally, the physical aspects of the model are compared to the SGN system and a multilayer model, demonstrating that VAM is comparable in physical accuracy to a two-layer model. • New reformulation of the Vertically Averaged and Moment (VAM) equations model. • Discretization with high order accurate finite. • volume finite-difference scheme. • The proposed approach is computationally very efficient and robust. • Successful comparison with analytical solutions and test problem with experimental reference data. [ABSTRACT FROM AUTHOR]

We study some properties of a multi-species degenerate Ginzburg–Landau energy and its relation to a cross-diffusion Cahn–Hilliard system. The model is motivated by multicomponent mixtures where cross-diffusion effects between the different species are taken into account, and where only one species does separate from the others. Using a comparison argument, we obtain strict bounds on the minimizers from which we can derive first-order optimality conditions, revealing a link with the single-species energy, and providing enough regularity to qualify the minimizers as stationary solutions of the evolution system. We also discuss convexity properties of the energy as well as long time asymptotics of the time-dependent problem. Lastly, we introduce a structure-preserving finite volume scheme for the time-dependent problem and present several numerical experiments in one and two spatial dimensions. [ABSTRACT FROM AUTHOR]

The article describes the thermo-hydraulic analysis of a dry cask storage building that is used for the storage of depleted nuclear fuel to determine the viability of a buoyancy driven cooling system. The analysis is performed in the form of steady-state CFD simulations. The resulting temperature distributions are them evaluated based on required operation criteria.

Abstract 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.

We present a technique to correct the cell-centered finite element scheme [20] (FECC) for full anisotropic diffusion problems on general meshes, which provides a discrete maximum principle (DMP). The correction scheme, named monotone nonlinear cell centered finite element scheme (MNFECC), is cell-centered in the sense that the solution can be computed from cell unknowns of the general primal mesh. Moreover, its coercivity and convergence are proven in a rigorous theoretical framework. Numerical experiments show that the method is effective and accurate, and it satisfies the discrete maximum principle.

Abstract From a visual point of view, volumetric information about reservoir portioning and communication such as sweep, flow patterns, and drainage zones are longer better interpreted and pictured when presented by an average volumetric flux calculation. To this hand, finite volume discretization can be used to substitute streamline simulation-based finite difference to assess flow diagnostic information. Herein, we use finite volume-based flow diagnostics to optimize waterflooding. In particular, we discretize in finite volume the flow equation from Darcy’s law single-phase incompressible flow steady state combining with two auxiliary flow equations, time of flight and stationary tracers using the two-point flux approximation to describe fluid particles motion and flow lines. In addition, with the estimation of dynamic heterogeneity, we compute the Lorenz coefficient to highlight the reservoir flow and storage capacity characterization. To optimize waterflooding rates, we first, use an objective function the equalized Lorenz coefficient got through the evaluation of average travel time in cells to increase sweep efficiency and decrease the dynamic heterogeneity coefficient. Second, following the same target, we use the flow diagnostic interactive tools to study the volumetric sweep displacement front and harmonize the flooding breakthrough. In this work, our conceptual approach is to see the reservoir initially filled with oil; then, optimizing the Lorenz coefficient leads us to an oil recovery improvement. To be pragmatic, we apply our waterflooding performance optimization model on two case studies, the ninth SPE comparative solution project, a reexamination of black-oil (synthetic case) and ZHNBA Chinese oilfield (real field dataset).

In this paper, we study a dissipation of solitary wave due to mangrove forest by using numerical simulation. Here, the solitary wave is chosen to represent tsunami wave form. To simulate the wave dynamic, we use the non-dispersive Nonlinear Shallow Water Equations (NSWE). The model is implemented numerically by using finite volume method in a momentum conservative staggered grid. By using the proposed numerical scheme, the numerical code is able to simulate solitary wave breaking phenomenon. Wave dissipation due to mangrove forest is modelled as bottom roughness with an approximate value of manning roughness, which is derived from the classical Morisson’s formula. To test the modelled dissipation by mangrove forest, we reconstruct a physical experiment in hydrodynamic laboratory where a solitary wave propagates above a sloping bottom, which has a parameterized mangrove in the shallower part. Two cases are performed to test the performance of the numerical implementation, i.e. the non-breaking and breaking solitary waves. Results of simulation agree quite well with the measurement data. The results of simulation are also analyzed quantitatively by calculating errors as well as correlation with the measurement data. Moreover, to investigate effects of wave steepness on solitary wave, to the reduction of wave energy, we perform numerical investigation. Various solitary waves with different wave steepness are simulated to see their effects on amplitude and energy reduction due to mangrove forest.

This study considers the accuracy of cell-to-face centre interpolation of convected quantities in unstructured finite volume meshes with cell-centred storage of variables. The accuracy of the interpolation algorithms were tested in isolation using ideal data to determine their numerical accuracy on both standard and artificially distorted meshes. It was found that the formally second- and third-order accurate interpolations based on one-dimensional interpolation along the line connecting the cells to the right and left of the face under consideration only have first-order accuracy in standard unstructured mesh, and less than first-order accuracy in distorted unstructured mesh. L1 interpolation errors in the distorted unstructured mesh are greater than in standard unstructured mesh. The order of accuracy and L1 errors can be improved by applying spatial corrections. The formally second-order accurate multi-dimensional interpolations tested in this study that are not based on one-dimensional interpolation along lines connecting the neighbour cells have first-order accuracy in both standard and distorted unstructured mesh. Linear interpolation between end vertices produces greatest L1 error in standard mesh; polynomial interpolation, linear interpolation between cell centres and standard QUICK produce the greatest L1 error in distorted mesh. Spatially correct QUICK, spatially correct linear interpolation between cell centres, Laplacian interpolation to face centres, and Taylor series expansion about an upstream cell produce the smallest L1 error in both standard and distorted mesh. Based on accuracy and the simplicity of implementation, Taylor series expansion about an upstream cell is the best choice for use in unstructured mesh.