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A Crank–Nicolson finite element method is proposed to solve the time-dependent Navier–Stokes equations. We prove that for a given smooth initial value, if a fully discrete finite element solution of the three-dimensional Navier–Stokes equations is bounded in a certain norm, then the strong solution of the Navier–Stokes equations satisfies uniqueness and smoothness. Further, the fully discrete solution converges to the strong solution as temporal step size τ → 0 and spatial step size h → 0 . [ABSTRACT FROM AUTHOR]

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier–Stokes equations posed on a passively evolving smooth closed surface embedded in \mathbb {R}^3. The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided. [ABSTRACT FROM AUTHOR]

A computational study has been performed to evaluate the use of jet impingement for cooling applications in the automotive industry. The current study uses an entire internal combustion engine cylinder with its components as a computational domain. An unsteady numerical solution for the Navier-Stokes equations was carried out using Improved Delayed Detached Eddy Simulation (IDDES). The volume of fluid approach is proposed to track and locate the liquid jet surface that is in contact with the air. The conjugate heat transfer approach is used to link the heat transfer solution between the fluid and the solid. The boundary conditions that are employed in the study are provided from lab experiments and one-dimensional simulations. The cooling jet in this study targets the hottest region in the piston, i.e., the region underneath the exhaust valve. Three nozzle sizes with flows at different Reynolds numbers are chosen to examine the thermal characteristics of the cooling jet. The computational study reveals that for a specific Reynolds number, the smaller diameter nozzle provides the highest heat transfer coefficient around the impingement point. The maximum relative velocity location at the impingement point slightly leads the location of the maximum Nusselt number. The maximum temperature in the piston decreases by 7% to 11% as the nozzle diameter changes from 1.0 to 3.0mm for a jet Reynolds number of 4,500. If a correct selection is made for the nozzle size, the cooling jet can be efficiently used to reduce the temperature and alleviate the thermal stresses in the piston in the region underneath the exhaust valve where the maximum temperature occurs. [ABSTRACT FROM AUTHOR]

A numerical simulation is conducted to study the flow of a three-dimensional incompressible wall jet. The study aims to determine the jet structure and to compare the propagation mechanisms of turbulent and laminar wall jets. The numerical solution of the Navier–Stokes equations in the turbulent case is obtained using the wall-resolved large eddy simulation. The simulation results are compared to experimental data. [ABSTRACT FROM AUTHOR]

The S-model kinetic equation is used to study the rarefied gas flow from a high-pressure tank to a low-pressure one through a flat membrane with a finite number of pores. The kinetic equation is solved numerically using a second-order accurate implicit conservative method implemented in the in-house code Nesvetay. For transitional and continuum flow regimes, numerical solutions of the compressible Navier–Stokes equations are obtained. The gas flow rate through the system of pores and the forces acting on the membrane bars are investigated as functions of the Knudsen number (Kn) at a pressure ratio of 2 : 1 in the tanks. The features of the flow field near the membrane and away from it are described. [ABSTRACT FROM AUTHOR]

The problem of determining the characteristics of a laminar swirling wall jet of an incompressible fluid is considered. Numerical solutions of the Navier–Stokes equations are obtained in the stationary and non-statitonary formulations. It is shown that the jet characteristics obey a self-similar law at large distances from the jet source, as in the case of a three-dimensional laminar non-swirling jet, but in our case the jet propagates at a certain angle to the initial direction of jet blowing. With a large swirling of flow in the jet, regions of recirculation flow appear and the jet flow becomes unsteady. [ABSTRACT FROM AUTHOR]

We introduce a surface finite element method for the numerical solution of Navier–Stokes equations on evolving surfaces with a prescribed deformation of the surface in the normal direction. The method is based on approaches for the full surface Navier–Stokes equations in the context of fluid‐deformable surfaces and adds a penalization of the normal component of the velocity. Numerical results demonstrate the same optimal order of convergence as proposed for surface (Navier–)Stokes equations on stationary surfaces. The approach is applied to high‐resolution three‐dimensional scans of clothed bodies in motion to provide interactive virtual fluid‐like clothing. [ABSTRACT FROM AUTHOR]

Significant thermochemical nonequilibrium effects always exist in the flow field around hypersonic vehicle at extreme flight condition. Previous studies have proposed various thermodynamic and chemical kinetic models to describe the thermochemical nonequilibrium processes in hypersonic and high-temperature flow. However, different selections from such models might lead to remarkable variations in computational burden and prediction accuracy, which is still a matter of being unclear. In the present study, different commonly studied models for calculating the thermochemical nonequilibrium are systematically evaluated. The 5-, 7- and 11-species chemical kinetic models of Dunn-Kang, Gupta and Park together with the one- and two-temperature models are employed respectively to simulate the hypersonic flows over a standard cylinder with the radius of 1 m by HyFLOW, which is a commercial software based on the numerical solution of Navier-Stokes equations. Three flight conditions of FIRE Ⅱ classical flight trajectory are employed in the study. It shows that the differences between the results of the Dunn-Kang, Gupta and Park chemical kinetic models with the same number of species are small, but the Gupta model predicts the most conservative values of the wall heat flux. When only the order of magnitude and distribution trends of the pressure and wall heat flux are concerned, the one-temperature model combined with 5-species chemical reaction model can be used for a rapid prediction. While the accurate flow solution is required, the two-temperature model conjugated with Gupta 11-species model is recommended, especially at the conditions of extremely high altitude and Mach number. [ABSTRACT FROM AUTHOR]

This paper describes the application of an adaptive mesh refinement (AMR) method to estimate centers of vortices of two-dimensional (2D) incompressible fluid flow over a wall-mounted plate. Following the accuracy verification of the AMR method using the benchmarks of 2D lid-driven cavity flows and backward-facing step flows, this study considers the application of the AMR method to the flow over a wall-mounted plate. The AMR method refines a mesh using numerical solutions of the Navier–Stokes equations computed using an open-source flow solver, Navier2D. The AMR is applied to seven test cases considering flows with different Reynolds numbers (1 0 ≤ Re ≤ 1 , 2 0 0) and the estimated centers of vortices after the plate are reported. The results show that AMR can capture the location of the center of vortices within the once refined cells. Furthermore, improved estimation of vortex centers is obtained using twice refined meshes. The AMR aims to get a refined mesh which captures the characteristics of flow with required accuracy at a lower computational cost. [ABSTRACT FROM AUTHOR]

Viscous particles of polymer melts and glasses coalesce under the action of surface tension. Resistance is due to viscosity, while inertia is not a contributing factor, with the Ohnesorge number being very high. Russian physicist Yakov Frenkel developed a model for neck growth during the initial stage of the merging process of two spherical particles, assuming uniform biaxial extensional flow. Frenkel's model was extended for prediction of neck size as a function of time to the completion of coalescence, expressed by an ordinary differential equation. The time t is expressed in dimensionless form as (tγ/ηR), where η, γ, and R denote the viscosity, surface tension, and particle radius, respectively. Models were also developed for viscoelastic effects, non‐isothermal conditions, and unequal diameter particles. For the coalescence of infinitely long cylinders, planar extensional flow is assumed. Other investigators presented numerical solutions of the Navier–Stokes equations, which include shear flow components, but the predictions of neck growth are not much different from those of the Frenkel‐based models. Comparisons to experiments are also discussed, involving polymers, glasses, animal tissue cells, and biomacromolecules. The models are also used in additive manufacturing applications for the determination of bonding and pore shrinkage. [ABSTRACT FROM AUTHOR]

The distinctive features of the flow velocity and temperature fields of ascending fluid flow in a metal round pipe (round casing string installed in a production well) under the conditions of its local induction heating are studied. The results of investigation are based on numerical solution of the Navier–Stokes equations in the Boussinesq–Oberbeck approximation. The calculations were performed using the Ansys Fluent software package (license ANSYS Academic Research CFD under the agreement with the Bashkir State University dated June 15, 2020). The fluid flow rates of 10 and 50 m3 per day are considered. Such flow rates correspond to the laminar and transitional flow regimes in the casing pipe. It is found that local perturbations of the velocity and temperature fields are presented in the near-wall region of the heated casing. Fluid temperature perturbations reach several Kelvin degrees, the local flow velocity which increases due to natural thermal convection in the near-wall region of the casing string being several times higher than the cross-section-average flow velocity. The occurrence of areas of vortex flow motion over the interval of induction heating due to natural thermal convection is shown. [ABSTRACT FROM AUTHOR]

Multi-parameter study on the subsonic equilibrium air plasma flows in the cylindrical discharge channel of an induction RF-plasmatron IPG-3 with the maximum operating power of 1 MW is presented. Simulations are carried out by numerical solution of full Navier–Stokes equations coupled with a two-dimensional equation for high-frequency electric field; the discretization of the equations is performed on a staggered Cartesian mesh. An effective method for calculation of the transport coefficients for ionized multi-component air (including the plasma conductivity) in the temperature range 300–15000 K is applied, with the higher-order approximations by the Sonine polynomial in the Chapman–Enskog method. Simulation results are presented, including the flow fields, electric field, and thermodynamic parameters of the air plasma in the discharge channel of a high-power induction plasmatron. The results obtained reveal for the first time the structure and parameters of a plasma torch in a large-diameter (200 mm) discharge channel at powers up to 300 kW, providing the axial specific enthalpies at the channel outlet as high as 68 MJ/kg. [ABSTRACT FROM AUTHOR]

The theory of a plane slowly changing recirculation flows is applied to solve the problems of flow around finite or semiinfinite plates with surfaces moving against the flow. The asymptotic flow structure is investigated and a numerical solution to the nonsteady-state Navier–Stokes equations is obtained. [ABSTRACT FROM AUTHOR]

At present, software products for numerical simulation of fluid dynamics problems (ANSYS Fluent, Ansys CFX, Star CCM, Comsol, etc.) problems are widely used. These software products are mainly based on the numerical solution of the Navier–Stokes equations, the most common and computationally easy method of solving, which is Reynolds averaging (RANS), and further closing the system using semi-empirical turbulence models. Currently, there are many modeling methods and turbulence models; however, there are no generalized recommendations for setting up grid models for modeling flows, while for practical use both the correct mathematical models and the setting of the computational grid are important. In particular, there are no generalized recommendations on the choice of scale of global elements of grid models for typical single channels. This work is devoted to the development and study of relations for a priori estimation of the parameters of a grid model in relation to solving hydrodynamic problems with fluid flow in channels. The paper proposes the introduction of a generalized grid convergence criterion for single channels at high Reynolds numbers. As single channels, a channel with a sudden expansion, a channel with a sudden contraction, and diffuser channels with different opening angles are considered. Based on the results of variant calculations of typical single channels at various Reynolds numbers and various geometric parameters, generalized criterion correlations were obtained to find dimensionless linear scales of grid elements relative to the hydrodynamic characteristics of the flow in the channel. Variant calculations of the compound channel were investigated, which showed the adequacy of correlations proposed. [ABSTRACT FROM AUTHOR]

The numerical modeling of transverse laminar flow past a new type of hollow-fiber membranes with external profiling has been performed. A model system of parallel fibers with symmetrical parallel protrusion obstacles or grooves is considered. The absorption of point particles (solute or gas molecules) from a laminar transverse flow of a viscous incompressible liquid (gas) is calculated for a row of fibers, and the dependences of the efficiency of retention of particles by fibers on the Peclet (Pe), Reynolds (Re), and Schmidt (Sc) numbers and on the distance between neighbor fibers in a row are determined. The flow velocity and concentration fields are calculated by numerical solution of the Navier–Stokes equations and the convective diffusion equation in a wide range of Peclet numbers Pe = 0.1 − 105 for Sc = 1, 10, 1000 and Re ≤ 100. [ABSTRACT FROM AUTHOR]

This work investigates flow and heat transfer under an array of annular jets impinging on a heated moving surface. Numerical solutions of the full Navier-Stokes equation were attempted with a highly refined mesh. This study reports results for Reynolds numbers up to 500. In the surface movement direction, a periodic element from a jet-bank configuration was chosen, and the nondimensional surface velocity was considered from zero (i.e., a stationary plate) to two times the jet velocity. The impact of annular jet impingement over a moving surface on flow and heat transfer characteristics, including the development of the flow field, velocity profiles, skin friction coefficient and topology of skin friction lines, and local as well as surface averaged Nusselt number distribution are presented. It is observed that both the flow field and thermal performance are strongly affected by the surface motion. Heat transfer from the surface initially increases with the increasing surface motion, and after attainment of the highest value, heat transfer reduces with a further increase in surface velocity. However, higher surface velocity leads to higher uniformity in heat transfer, which may be beneficial for situations demanding uniformity in heat transfer. [ABSTRACT FROM AUTHOR]

It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier-Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables the use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed-boundary method is used to deal with general geometries involving the fluid-structure interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier-Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier-Stokes equations solver uses second-order central FDM and Quadratic Upstream Interpolation for Convective Kinematics scheme for the discretization of the diffusion term and advection term, respectively, which may be replaced by other higher-order schemes to further improve the accuracy. [ABSTRACT FROM AUTHOR]

The accurate prediction of aerodynamic properties is an essential requirement for the design of applications that involve fluid flows, especially in the aerospace industry. The aerodynamic characteristics of fluid flows around a wing or an airfoil are usually forecasted using the numerical solution of the Reynolds-averaged Navier–Stokes equation. However, very heavy computational expenses and lengthy progression intervals are associated with this method. Advancements in computational power and efficiency throughout the present era have considerably reduced these costs; however, for many practical applications, performing numerical simulations is still a very computationally expensive and time-consuming task. The application of machine learning techniques has seen a sharp rise in various fields over recent years, including fluid dynamics, and they have proved their worth. In the present study, a famous machine learning model that is known as the back-propagation neural network was implemented for the prediction of the aerodynamic coefficients of airfoils. The most important aerodynamic properties of the coefficient of lift and the coefficient of drag were predicted by providing the model with the name, flow Reynolds number, Mach number and the angle of attack of the airfoils with respect to the incoming flows as input parameters. The dataset for the current study was obtained by performing CFD simulations using the RANS-based Spalart–Allmaras turbulence model on four different NACA series airfoils under varying aerodynamic conditions. The data that were obtained from the CFD simulations were divided into two subsets: 70% were used as training data and the remaining 30% were used as validation and testing data. The BPNN showed promising results for the prediction of the aerodynamic coefficients of airfoils under different conditions. An RMSE value of 3.57 × 10−7 was achieved for the best performance validation case with 28 epochs when there were 10 neurons in the hidden layer. The regression plot also depicted a close to perfect fit between the predicted and actual values for the regression curves. [ABSTRACT FROM AUTHOR]

A convection system can be designed as an energy-efficient one by making a considerable reduction in exergy losses. In this context, entropy generation analysis is performed on the infrared suppression system numerically. In addition, results due to heat transfer are also shown. The numerical solution of the Navier-stokes equation, energy equation, and turbulence equation is executed using ansysfluent 15.0. To perform the numerical analysis, different parameters such as the number of funnels, Rayleigh number (Ra), inner surface temperature, and geometric ratio are varied in the practical range. Results are shown in terms of heat transfer, entropy generation, irreversibility (due to heat transfer and fluid friction), and Bejan number with some relevant parameters. Streamlines and temperature contours are also provided for better visualization of temperature and flow field around the device. Results show that heat transfer and mass flow rate increase with the increase in the number of funnels. Entropy generation and the irreversibility rise with an increase in the number of funnels and geometric ratio. Also, the Bejan number decreases with an increase in Ra and the number of funnels. A cooling time is also obtained using the lumped capacitance method. [ABSTRACT FROM AUTHOR]

Transonic flows at high Reynolds numbers can lead to high dynamic pressures and, consequently, to aerostructural deflections of aircraft structures. This study aims to develop and validate a high-fidelity static aeroelastic analysis environment that is efficient and that can be used in an industrial setting. The aerodynamics is represented by numerical solutions of the Reynolds-averaged Navier-Stokes equations with appropriate turbulence closures. The load transfer process uses finite element shape functions in order to distribute the aerodynamic loads into the structural discretization. The structural analysis employs a modal basis approach, and a wingtip deflection convergence study is performed to find an adequate modal basis size. Radial basis functions are used for the fluid mesh displacement, and the influence of the support radius is evaluated to determine the optimal values relative to the wing mean aerodynamic chord. The capability is tested using the static aeroelastic benchmarks of the High Reynolds Aerostructural Dynamics Project (HIRENASD) and NASA's Common Research Model (CRM). The static aeroelastic results demonstrate robustness and consistency for the aerodynamic coefficients, pressure distributions, and structural deflection predictions at different normalized dynamic pressure values and grid refinement levels. • The paper describes the development and testing of a novel framework for performing static aeroelastic analyses. • Detailed studies of static aeroelastic behavior of the HIRENASD and the NASA CRM configurations are presented. • The work demonstrated the importance of structural flexibility in aerodynamic moment coefficients for wind tunnel models. • Guidelines for an adequate support radius for mesh movement in static aeroelastic applications using RBFs are presented. [ABSTRACT FROM AUTHOR]

Given a full space-time-varying structure function Graph $\mathcal {S}(r,t)$ we can construct the time-varying structure function that would be derived from a time series obtained by an observer moving with constant velocity Graph $V$: this correspond to mapping a cut in the space-time-varying structure function along the line Graph $r = V t$. For large Graph $r$ outside the inertial range, the structure function will approach the value Graph $2 u {rms}^2$, with Graph $u {rms}$ again being the root-mean-square value of the velocity component chosen for the structure function. Given a randomly varying velocity field Graph $\boldsymbol {u}$ with components Graph $u j(\boldsymbol {r},t)$, Graph $j = 1,2,3$ and Graph $\boldsymbol {r}=\{r 1,r 2,r 3\}$, we can formulate Taylor's hypothesis by referring to a frame of reference moving with a known velocity Graph $\boldsymbol {V}$ to give a time series Graph $u j(\boldsymbol {r} 0 + \boldsymbol {V} t,t)$. The resulting function Graph $\mathcal {S}(Vt,t)$ can be shown as a function of Graph $t$ or, as turns out to be more convenient, as a function of Graph $r = V t$. For Graph $r\rightarrow 0$ the difference between the transverse Graph $\mathcal {G}$ and longitudinal Graph $\mathcal {S}$ structure functions vanishes, and the ratio Graph $(2 \mathcal {G} + \mathcal {S})/\mathcal {S} \rightarrow 3$ for all times Graph $t > 0$. [Extracted from the article]

The paper considers practical aspects of mathematical modeling in predictions of the level of near-field pressure pulsations of a near-future prototype supersonic business aircraft. A numerical modeling technique based on the numerical solution of the Navier-Stokes equations is proposed. The method is verified by near-field simulations of the NASA C608 supersonic low-boom demonstrator. We consider a supersonic flight with M=1.4 at a flight altitude of 16,215 m. Good convergence of our predictions with experimental data and results of other researchers is shown. Near-field sonic-boom simulations of the prototype supersonic business aircraft are used to illustrate how the method can be applied in practice for building a second-generation supersonic passenger aircraft. Two aerodynamic configurations of the aircraft are considered: no-tail and canard no-tail. The canard no-tail configuration in the as-is aircraft dimension and design was found to have no advantages over the no-tail configuration in the level of its near-field pressure pulsations because of its nonoptimality. Further recommendations for solving the near-field sonic-boom minimization problem are related to the construction of a comprehensive mathematical model enabling coupled simulations due to smooth integration of a parametrized aircraft geometry, an aerodynamic solver, and an optimizer. [ABSTRACT FROM AUTHOR]

In this work, we have proposed a numerical approach for solving the incompressible Navier–Stokes equations in the streamfunction‐vorticity formulation. The numerical scheme is based on the diagonally implicit fractional‐step θ−(DIFST) method used for the time discretization and the conforming finite element method for the spatial discretization. The accuracy and efficiency of the scheme are validated by solving some benchmark problems. The numerical simulations are carried out using the DUNE‐PDELab open‐source software package. The comparison of DIFST scheme with different time discretization schemes is provided in terms of CPU time. Also, different solvers with preconditioners are investigated for solving the resulting algebraic system of equations numerically. [ABSTRACT FROM AUTHOR]

Poisson equation lies in the heart of the numerical solutions of incompressible Navier–Stokes equations (NSEs) based on the popular projection methods, which decouple the pressure and velocities fields. This paper presents enhanced numerical solutions of the 2D incompressible NSEs inspired by a newly-developed Generalized Harmonic Polynomial Cell (GHPC) method for the Poisson equation, which has a fourth-order spatial accuracy. To achieve that, the original GHPC method is adapted to accommodate immersed boundaries, necessary when a staggered grid for velocities and pressure is applied. The finite difference method (FDM) is used in the spatial discretization of the diffusion and advection terms. Numerical analyses of lid-driven cavity flow, a Taylor–Green vortex, and flow around a smooth circular cylinder all show encouraging results, confirming the accuracy and efficiency of the new solver. Through comparison with an NSEs solver which applies second-order FDM for the Poisson equation, we demonstrate that the accuracy of the pressure solution can be greatly improved by applying the more accurate GHPC method for the Poisson equation, even though the accuracy of the velocities solutions are limited by the numerical schemes for advection–diffusion equations. The accuracy in the pressure solution can also be translated into CPU time saving to achieve a predefined accuracy. The present immersed-boundary GHPC Poisson equation solver can easily be 'plugged' into other existing NSEs solvers utilizing staggered grids. • A new 2D Navier–Stokes equations solver based on generalized harmonic polynomial cell (GHPC) method. • Immersed-boundary strategy introduced in the original GHPC method. • Demonstration of the enhanced pressure field solution by using the new solver. [ABSTRACT FROM AUTHOR]

The total enthalpy of a uniform flow is redistributed behind a thermally insulated body such that a considerable cooling of fluid in terms of total temperature occurs near the wake centreline. This energy separation phenomenon is also observed after time averaging and can lead to the recovery temperature at the rear part of the body becoming lower than the static temperature of the incoming flow (the Eckert-Weise effect). By the numerical solution of the Navier-Stokes equations, the present work studies energy separation in the wake, the Eckert-Weise effect and their sensitivity on the flow interference behind side-by-side cylinders. The considered distances between the cylinders cover the key regimes of interference: single, bistable and coupled vortex streets. The first and second regimes amplify the efficiency of energy separation in the wake and the intensity of the Eckert-Weise effect, respectively. In the developed wake, a clear relation between the vortex structure and the total enthalpy redistribution is demonstrated as well as a limitation on the intensity of this redistribution imposed by the deficit of velocity. The connection of the Eckert-Weise effect with the vortex formation process is clarified. Among the mechanisms changing the total enthalpy in fluid particles, the non-stationarity of pressure defines the averaged distribution: the decrease of pressure in forming vortices is mainly responsible for the cooling of fluid behind the body. The balance with the heating of the rear surface by the involvement of fluid from the sides defines the intensity of the effect. [ABSTRACT FROM AUTHOR]

The acoustic behavior of individual slits within microslit absorbers (MSAs) is investigated to explore the influence of porosity, edge geometry, slit position, and plate thickness. MSAs are plates with arrays of slit-shaped perforations, with the height of the order of the acoustic viscous boundary layer thickness, for optimized viscous dissipation. Due to hydrodynamic interaction, each slit behaves as confined in a rectangular channel. The flow within the slit is assumed to be incompressible. The viscous dissipation and the inertia are quantified by the resistive and the inertial end-corrections. These are estimated by using analytical results and numerical solutions of the linearized Navier–Stokes equations. Expressions for the end-corrections are provided as functions of the ratio of the slit height to viscous boundary layer thickness (shear number) and of the porosity. The inertial end-correction is sensitive to the far-field behavior of the flow and for low porosities strongly depends on the porosity, unlike for circular perforations. The resistive end-correction is dominated by the edge geometry of the perforation. The relative position of the slit with respect to the wall of the channel is important for distances to the wall on the order of the slit height. The plate thickness does not have a significant effect on the end-corrections. [ABSTRACT FROM AUTHOR]

Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method refines a mesh using the numerical solution of the Navier–Stokes equations computed on the mesh by an open source software Navier2D which implemented a vertex centered finite volume method (FVM) using the median dual mesh to form control volumes about each vertex. The accuracy is shown by the comparison between vortex center locations calculated from the linearly interpolated numerical solutions and those obtained in the benchmark. The AMR method is proposed based on the qualitative theory of differential equations, and it can be applied to refine a mesh as many times as required and used to seek accurate numerical solutions of the mathematical models including the continuity equation for incompressible fluid or steady-state compressible flow with low computational cost. [ABSTRACT FROM AUTHOR]

A comprehensive numerical study is performed on a vertical hollow cylinder of finite thickness for natural convection with surface radiation effect. The prime aim is to find out the heat transfer rate due to both natural convection and radiation from both the inner and outer walls of the tube. Also, an attempt is made to estimate the cooling time, the time required to bring down the cylinder temperature from a prescribed temperature to atmospheric temperature. Numerical solution of Navier-Stokes equation, energy equation, and radiation equation is solved, taking the finite volume approach of ANSYS-Fluent 18 around a vertical tube for determining flow and heat transfer characteristics around it. Different relevant parameters are chosen for the numerical analysis, such as Rayleigh number (from 5.7 × 103 to 5.7 × 107), inner surface temperature (from 350 K to 550 K), and aspect ratio (L/D) of the tube (from 0.5 to 20). To catch the effect of surface radiation, emissivity (from 0 to 1) is also varied. A comparison is made for natural convection and fluid flow characteristics with and without surface radiation effect. [ABSTRACT FROM AUTHOR]

The Lamb dipole is a steady translating structure in 2D ideal fluid flow with opposite-sign vorticity of compact support in a circular disk. Previous studies have shown that when viscosity is present, the resulting viscous Lamb dipole develops a head-tail structure in which the head expands in size, while a tail of low amplitude vorticity is left behind as the head moves forward; in addition, the maximum vorticity and total circulation on each side of the dipole decay in time. Here we examine these decay properties by comparing numerical solutions of the Navier–Stokes equation (NSE) and diffusion equation (DE) in the Reynolds number range using the inviscid Lamb dipole as initial condition; this enables us to compare the combined effects of convection and diffusion in the NSE with the sole effect of diffusion in the DE. The results show that for a given Re, the vortex core size, shape, and maximum vorticity are nearly the same for the NSE and DE, indicating that convection has little effect on these properties. Nonetheless, compared to the DE, convection in the NSE inhibits circulation decay at low Re, while it enhances circulation decay at high Re, and the lateral separation of the vortex cores is a critical factor in this transition. [ABSTRACT FROM AUTHOR]

This paper presents the radial basis function (RBF) approximation for the numerical solution of Stokes and Navier-Stokes equations in a constricted enclosure under the effect of magnetic field with different orientations. RBFs are used for the approximation of the particular solution which becomes also the approximate solution of the problem satisfying the boundary conditions. Numerical results are obtained for several values of Hartmann number and constriction ratio. As the strength of the horizontally applied magnetic field increases, Stokes flow extends covering the whole pipe. Applied magnetic field in the pipe-axis direction generates the electric potential exhibiting behavior similar to streamlines. When the constriction ratio increases, flow squeezes through the left wall regardless of the direction of the magnetic field. [ABSTRACT FROM AUTHOR]

We investigate the self-propulsion of an inertial swimmer in a linearly density stratified fluid using the archetypal squirmer model which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution of the Navier–Stokes equations using the finite volume method for solving the fluid flow and the distributed Lagrange multiplier method for modelling the swimmer. The simulations are performed for Reynolds numbers ($Re$) between 5 and 100 and Froude numbers ($Fr$) between 1 and 10. We find that increasing the fluid stratification strength reduces the swimming speeds of both pushers and pullers relative to their speeds in a homogeneous fluid. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. With increasing the stratification, the isopycnals tend to deform less, which offers resistance to the flow generated by the squirmers around them to propel themselves. This resistance increases with stratification, thus, reducing the squirmer swimming velocity. Stratification also stabilizes the flow around a puller keeping it axisymmetric even at high $Re$ , thus, leading to stability which is otherwise absent in a homogeneous fluid for $Re$ greater than $O(10)$. On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady and three-dimensional, which is otherwise steady and axisymmetric in a homogeneous fluid. A pusher is a more efficient swimmer than a puller owing to efficient convection of vorticity along its surface and downstream. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers. [ABSTRACT FROM AUTHOR]

A numerical solution of the Navier–Stokes equations describing the instability of a two-dimensional subsonic flow about a flat plate is presented. It is obtained with the 16th-order multioperators-based scheme without introducing artificial exciters. It shows how small numerical disturbances produced by the scheme generate downstream from the leading edge a succession of wave packets formed by the Tollmien–Schlichting waves. When travelling downstream, the packets demonstrate high amplification rates and the occurrence of separation bubbles. The details of their coming into being, the spatial–temporal progress and the spectra are described. [ABSTRACT FROM AUTHOR]

The receptivity of the Blasius boundary layer over a semi-infinite flat plate with an elliptic leading edge and of aspect ratio five was investigated using a direct numerical solution of two-dimensional Navier-Stokes equations. The result of the computation where the slip condition is applied to the fluctuating component of velocity at the wall surface is compared with that of an ordinary computation using a nonslip condition. Another numerical experiment is performed where no vorticity fluctuation is supplied from a freestream while prerecorded values of vorticities at the wall in response to the passage of convecting fluctuations are used as the wall vorticity boundary condition. It is shown that vorticity fluctuations in the boundary layer can be classified according to their wavelengths. Waves with longer wavelengths originate from the freestream, whereas waves with shorter wavelengths close to T-S waves originate from the surface of the plate. In another numerical experiment, the slip boundary condition against the fluctuation component of vorticity is applied to the limited area of the wall surface. The aim of the study is to determine the part of the elliptic leading edge or flat plate that induces vorticity fluctuations, thereby resulting in the creation of T-S waves. The numerical results show that the contribution of vorticity fluctuations originating from the juncture is the most crucial, whereas the vorticities supplied in the elliptic leading-edge surface negatively affect the amplitude of vorticity fluctuations inside the boundary layer. And, the stagnation section did not show positive contribution. [ABSTRACT FROM AUTHOR]

In this study, the dual mesh control domain method, which employs the finite element approximation of the primary variables and the finite volume idea of satisfying the governing equations over a control domain, is used for the numerical solution of the Navier–Stokes equations governing the flows of viscous incompressible fluids using the penalty function formulation for two-dimensional analysis. The primal mesh is the mesh of finite elements used to interpolate the velocity field, while the dual mesh of control domains is used to satisfy the integral form of the Navier–Stokes equations, and thus, the method shares certain desirable features of the two popular methods. Numerical examples involving nonlinear Poisson's equation and the Navier–Stokes equations are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions, the latter depending on the scheme used to solve the discretized equations. [ABSTRACT FROM AUTHOR]

We study the flow of a viscous incompressible liquid in a cylindrical duct with two serial diaphragms by finding the numerical solutions of nonstationary Navier–Stokes equations. It is shown that, within a certain range of Reynolds numbers, the flow of liquid in the region between the diaphragms is characterized by the presence of an unstable shear layer. A series of sequential vortices formed in the shear layer generates self-sustained oscillations of the velocity profile in the opening of the second diaphragm. It is shown that the analyzed system also has two stable modes of periodic oscillations with different frequencies. These oscillations may play the role of an acoustic source in the duct. [ABSTRACT FROM AUTHOR]

The improved understanding of complex interactions of marine ecosystem components makes the use of fully coupled hydrodynamic, biogeochemical and individual based models more and more relevant. At the same time, the increasing complexity of the models and diverse user backgrounds calls for improved user friendliness and flexibility of the model systems. We present FlexSem, a versatile and user-friendly framework for 3D hydrodynamic, biogeochemical, individual based and sediment transport modelling. The purpose of the framework is to enable natural scientists to conduct advanced 3D simulations in the marine environment, including any relevant processes. This is made possible by providing a precompiled portable framework, which still enables the user to pick any combination of models and provide user defined equation systems to be solved during the simulation. We here present the ideas behind the framework design, the implementation and documentation of the numerical solution to the Navier-Stokes equations in the hydrodynamic module, the surface heat budget model, the pelagic and benthic equation solvers and the Lagrangian movement of the agents in the agent based model. Five examples of different applications of the system are shown: 1) Hydrodynamics in the Disko Bay in west Greenland, 2) A biogeochemical pelagic and benthic model in the inner Danish waters, 3) A generic mussel farm model featuring offline physics, food levels and mussel eco-physiology, 4) Sediment transport in Clarion-Clipperton zone at the bottom of the Pacific and 5) Hydrodynamics coupled with an agent based model around Zanzibar in Tanzania. Hence we demonstrate that the model can be set up for any area with enough forcing data and used to solve a wide range of applications. [ABSTRACT FROM AUTHOR]

Diverterless supersonic inlet integration for a flight vehicle requires a three-dimensional compression surface (bump) design with an acceptable shock structure and boundary layer diversion; this results in a low drag induction system with acceptable propulsive efficiency. In this investigation, a computational fluid dynamics-based-generated bump is used to design an integrated diverterless supersonic inlet without any bleed mechanism on a forebody with a large wetted area. Numerical solution of the Navier–Stokes equations simulates the flow pattern of the configuration. The forebody design analysis includes simulating the effects of angle of attack and sideslip by dependent computational domains. Results demonstrate the ability of the bump surface to keep the shock structures in an operational mode even at high supersonic angles of attack. Analysis of shock structures and shock wave boundary layer interactions at supersonic maneuver conditions indicate that the aerodynamic efficiency of the diverterless supersonic inlet in conditions with a thick boundary layer and high angles of attack is sufficient to ensure operation throughout the supersonic flight envelope. [ABSTRACT FROM AUTHOR]

We present a multiscale computational framework for high-pressure resin transfer molding of fiber-reinforced composites. Due to the relatively rapid speed of resin flow and the significant convective effects, this process is governed by the nonlinear steady-state Navier–Stokes equations, as opposed to the linear Stokes equations commonly adopted for the simulation of classical resin transfer molding processes. To overcome the computational challenge of directly solving the high-pressure resin filling problem through the fiber preform, we developed a data-driven nonlinear homogenization approach where the average velocity and instantaneous permeability computed from the microscale representative volume element problem provide solution-dependent coefficients for the macroscale problem. The proposed data-physics driven computational framework has been validated against the direct numerical solution of the steady-state Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

• Head-on ternary droplet collision is investigated numerically. • The shape evolution and energy change of head-on ternary droplet collision are described. • The axial and radial geometrical characteristic of head-on ternary droplet collision are analyzed. • The effect of the Weber number, central droplet size and distance offset on the head-on ternary droplet collision are investigated. In recent years, ternary droplet collision has been proposed in some new application prospects, such as three-dimensional (3D) reactive inkjet printer. To better apply ternary droplet collision, head-on ternary droplet collision of same liquid in the gaseous environment is investigated numerically. The investigation is based on the finite volume numerical solution of the Navier–Stokes equations in axisymmetric form. Volume of Fluid (VOF) methodology and adaptive grid technique are used to capture the liquid-gas interface and the reliability of the methodology is verified by published experimental data. Head-on ternary droplet collision for a wide range of Weber number is studied. The shape and velocity field evolution of three colliding droplets (coalescence and separation) is described in detail. Moreover, the time evolution of the kinetic energy and the surface energy of three colliding droplets, the viscous dissipation and the maximum deformation are evaluated. Furthermore, based on the dimensionless flow parameters, relevant correlations determining the length of ligament, the maximum diameter of ligament, the length of bridge and the maximum radial length are also presented quantitatively. Finally, the effect of central droplet size and distance offset on the head-on ternary droplet collision are investigated, the results are also compared and analyzed. It is believed that the present work is meaningful for better applying ternary droplet collision. [ABSTRACT FROM AUTHOR]

In this paper the numerical solution of the fractional Navier–Stokes equations (FNSE) is derived by means of a new non-standard finite difference method (NSFDM). The fractional differential operators are taken in sense of the Riesz fractional derivative. The pressure driven by the flow between two parallel plates is solved with the NSFDM and a modified trapezoidal quadrature rule of fractional order. The stability and convergence of the proposed scheme are proved. Numerical examples illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Partial texturing of the surface of journal bearings have been proven very beneficial in terms of friction coefficient. In the present work, the load support of the hydrodynamic textured journal bearing combined with artificial slippage is fully characterized by means of computational fluid dynamics (CFD) simulations based on the numerical solution of the Navier-Stokes equations for incompressible flow. In order to model slippage, the enhanced user-defined-function (UDF) code is developed. Realistic boundary condition is employed by implementing the mixture multiphase model to model a cavitation in the bearing. The numerical analysis is performed under the condition of different groove depths, eccentricity ratios and slippage placements along the textured area of bearing. The simulation results including hydrodynamic pressure and load support are gained and compared for conventional smooth parameters. A reference to determine optimal groove depths as well as best artificial slippage placement of textured bearing under different conditions of loading are proposed. Based on the present results, favorable slippagetextured journal bearing design can be assessed. [ABSTRACT FROM AUTHOR]

Mechanisms affecting the transition to three-dimensionality in a cylinder wake are studied based on the local description of the perturbations development for modes A and B. Early stages of three-dimensional vortex structures growth are simulated by the direct numerical solution of the Navier–Stokes equations. The influence of basic mechanisms (such as vorticity diffusion, stretching and tilting of vortex lines) on the growth and decay of perturbations in fluid particles, and on the change in the direction of generated longitudinal vorticity vectors is considered. The same analysis is carried out for an idealized elliptic flow, which reveals qualitative similarities and differences in the perturbations development inside the forming vortex and for the flow with elliptical streamlines. It was shown that the line, along which perturbations of mode B concentrate, can be approximately found based on a two-dimensional solution. The instability of mode B is studied by introducing a simplified two-dimensional flow, which approximates the flow in the braid shear layer. Based on the linear stability analysis of this flow it can be assumed that the curvature of the braid shear layer plays an important role in the mode B instability. • The initial stages of 3D wake transition are considered for modes A and B. • The development of perturbations in fluid particles is described. • The simplified approximation for the braid shear layer flow is constructed. • The linear instability of this flow is sensitive to its curvature. [ABSTRACT FROM AUTHOR]