Showing papers in "International Journal for Numerical Methods in Fluids in 2004"
TL;DR: In this article, a new stabilized finite element method for the Stokes problem is presented by modifying the mixed variational equation by using local L 2 polynomial pressure projections, which leads to a stable variational formulation.
Abstract: A new stabilized finite element method for the Stokes problem is presented. The method is obtained by modification of the mixed variational equation by using local L2 polynomial pressure projections. Our stabilization approach is motivated by the inherent inconsistency of equal-order approximations for the Stokes equations, which leads to an unstable mixed finite element method. Application of pressure projections in conjunction with minimization of the pressure–velocity mismatch eliminates this inconsistency and leads to a stable variational formulation.
Unlike other stabilization methods, the present approach does not require specification of a stabilization parameter or calculation of higher-order derivatives, and always leads to a symmetric linear system. The new method can be implemented at the element level and for affine families of finite elements on simplicial grids it reduces to a simple modification of the weak continuity equation. Numerical results are presented for a variety of equal-order continuous velocity and pressure elements in two and three dimensions. Copyright © 2004 John Wiley & Sons, Ltd.
352 citations
TL;DR: In this article, the authors present a numerical study of a two-dimensional time-dependent flow around a cylinder and provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time.
Abstract: We present a numerical study of a two-dimensional time-dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied
226 citations
TL;DR: In this paper, a wetting-drying condition (WDC) for unsteady shallow water flow in two dimensions leading to zero numerical error in mass conservation is presented.
Abstract: A wetting-drying condition (WDC) for unsteady shallow water flow in two dimensions leading to zero numerical error in mass conservation is presented in this work. Some applications are shown which demonstrate the effectiveness of the WDC in flood propagation and dam break flows over real geometries. The WDC has been incorporated into a cell centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured meshes. Previous wetting-drying condition based on steady-state conditions lead to numerical errors in unsteady cases over configurations with strong variations on bed slope. A modification of the wetting-drying condition including the normal velocity to the cell edge enables to achieve zero numerical errors. The complete numerical technique is described in this work including source terms discretization as a complete and efficient 2D river flow simulation tool
211 citations
TL;DR: The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes, giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised.
Abstract: The method of manufactured solutions is used to verify the order of accuracy of two finite-volume Euler and Navier–Stokes codes. The Premo code employs a node-centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second-order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd.
173 citations
TL;DR: In this paper, an analysis of the mass and normal-momentum conservation at a liquid-vapour interface is conducted in the context of homogeneous equilibrium flow theory, resulting in a new interfacial dynamics-based cavitation model.
Abstract: The merits of transport equation-based models are investigated by adopting an enhanced pressure-based method for turbulent cavitating flows. An analysis of the mass and normal-momentum conservation at a liquid–vapour interface is conducted in the context of homogeneous equilibrium flow theory, resulting in a new interfacial dynamics-based cavitation model. The model offers direct interpretation of the empirical parameters in the existing transport-equation-based models adopted in the literature. This and three existing cavitation models are evaluated for flows around an axisymmetric cylindrical body and a planar hydrofoil, and through a convergent–divergent nozzle. Although all models considered provide qualitatively comparable wall pressure distributions in agreement with the experimental data, quantitative differences are observed in the closure region of the cavity, due to different compressibility characteristics of each cavitation model. In particular, the baroclinic effect of the vorticity transport equation plays a noticeable role in the closure region of the cavity, and contributes to the highest level of turbulent kinetic energy there. Copyright © 2004 John Wiley & Sons, Ltd.
159 citations
TL;DR: A new modelling technique is introduced that couples Navier–Stokes equations with protein molecular dynamics to investigate the behaviours of RBC aggregates and their effects on the blood rheology and explains the shear‐rate‐dependence of the blood viscoelastic properties.
Abstract: SUMMARY The red blood cell (RBC) aggregation plays an important role in many physiological phenomena, in particular the atherosclerosis and thrombotic processes. In this research, we introduce a new modelling technique that couples Navier-Stokes equations with protein molecular dynamics to investigate the behaviours of RBC aggregates and their eects on the blood rheology. In essence, the Lagrangian solid mesh, which represents the immersed deformable cells, is set to move on top of a background Eulerian mesh. The eects of cell-cell interaction (adhesive =repulsive) and hydrody- namic forces on RBC aggregates are studied by introducing equivalent protein molecular potentials into the immersednite element method. The aggregation of red blood cells in quiescentuids is simulated. The de-aggregation of a RBC cluster at dierent shear rates is also investigated to pro- vide an explanation of the shear-rate-dependence of the blood viscoelastic properties. Finally, the in- �uences of cell-cell interaction, RBC rigidity, and vessel geometry are addressed in a series of test cases with deformable cells (normal and sickle RBCs) passing through micro- and capillary vessels. Copyright ? 2004 John Wiley & Sons, Ltd.
150 citations
TL;DR: In this paper, a mesh-adaptation algorithm is applied to the Eulerian Lagrangian model of a non-linear solid and a Lagrange multiplier to adjust the position of the nonlinear solid mesh every time step, which makes it possible to sustain a physiological pressure gradient across a solid mesh.
Abstract: SUMMARY A new approach for modelling theuid-structure interaction ofexible heart valves is proposed. Using anite element method, a Lagrangian description of a non-linear solid and an Eulerian description of auid are coupled by a Lagrange multiplier. This multiplier allows the solid anduid mesh to be non-conform. Solid displacements anduid velocities are described well in such actitious domain approach. However, the accuracy of pressures and shear stresses in the vicinity of the solid are poor. Therefore an inexpensive mesh-adaptation algorithm is applied, which adapts theuid mesh to the position of the solid mesh every time step. This minor adjustment of theuid mesh makes it possible to sustain a physiological pressure gradient across a solid leaet. Furthermore, shear stresses can be computed at both sides of the leaet. The method is demonstrated for a 2D example, however with a scope to 3D modelling. Copyright ? 2004 John Wiley & Sons, Ltd.
132 citations
TL;DR: In this paper, a reliable and automated approach to the generation of unstructured hybrid grids comprised of tetrahedra, prisms and pyramids for high Reynolds number viscous flow simulations is presented.
Abstract: This paper presents a reliable and automated approach to the generation of unstructured hybrid grids comprised of tetrahedra, prisms and pyramids for high Reynolds number viscous flow simulations. To enhance robustness, the hybrid mesh generation process starts with the formation of an isotropic tetrahedral grid. Prismatic layers are then added on no-slip walls fully automatically by obeying user-specified boundary conditions and three parameters: the number of the layers, an initial layer thickness normal to the walls, and a stretching factor. Topological modifications to the original isotropic tetrahedral elements are prohibited during the layer generation process. The tetrahedral elements near no-slip walls are shifted inward and the resulting gap between the tetrahedra and the walls is filled up with prismatic elements. To enhance the quality of the prismatic layers around sharp corners, two normals are evaluated for the marching process in these regions. The addition of prismatic elements is locally stopped if negative-volume elements are created or not enough space is left. An angle-based smoothing method ensures that the quality of the tetrahedral elements is retained for a reasonable computational cost. The method is demonstrated for two scaled experimental supersonic airplane models designed at the National Aerospace Laboratory of Japan (NAL). Numerical results are compared with wind tunnel experimental data. Copyright © 2004 John Wiley & Sons, Ltd.
118 citations
TL;DR: In this paper, the Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) scheme is used to evaluate interface fluxes in both wet- and dry-bed applications.
Abstract: Flooding due to the failure of a dam or dyke has potentially disastrous consequences. This paper presents a Godunov-type finite volume solver of the shallow water equations based on dynamically adaptive quadtree grids. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) scheme is used to evaluate interface fluxes in both wet- and dry-bed applications. The numerical model is validated against results from alternative numerical models for idealized circular and rectangular dam breaks. Close agreement is achieved with experimental measurements from the CADAM dam break test and data from a laboratory dyke break undertaken at Delft University of Technology. Copyright © 2004 John Wiley Sons, Ltd.
116 citations
TL;DR: In this article, the Navier-Stokes conservation equations of the flow field are numerically solved on two-dimensional axisymmetric or three-dimensional unstructured grids, using Cartesian velocity components, following the finite volume approximation and a pressure correction method.
Abstract: The volume of fluid (VOF) method is used to perform two-phase simulations (gas–liquid). The governing Navier–Stokes conservation equations of the flow field are numerically solved on two-dimensional axisymmetric or three-dimensional unstructured grids, using Cartesian velocity components, following the finite volume approximation and a pressure correction method. A new method of adaptive grid local refinement is developed in order to enhance the accuracy of the predictions, to capture the sharp gas–liquid interface and to speed up the calculations. Results are compared with experimental measurements in order to assess the efficiency of the method. Copyright © 2004 John Wiley & Sons, Ltd.
105 citations
TL;DR: In this article, a spectral/hp element discontinuous Galerkin model for simulating shallow water flows on unstructured triangular meshes is presented, which uses an orthogonal modal expansion basis of arbitrary order for the spatial discretization and a third-order Runge-Kutta scheme to advance in time.
Abstract: We present a spectral/hp element discontinuous Galerkin model for simulating shallow water flows on unstructured triangular meshes. The model uses an orthogonal modal expansion basis of arbitrary order for the spatial discretization and a third-order Runge–Kutta scheme to advance in time. The local elements are coupled together by numerical fluxes, evaluated using the HLLC Riemann solver. We apply the model to test cases involving smooth flows and demonstrate the exponentially fast convergence with regard to polynomial order. We also illustrate that even for results of ‘engineering accuracy’ the computational efficiency increases with increasing order of the model and time of integration. The model is found to be robust in the presence of shocks where Gibbs oscillations can be suppressed by slope limiting. Copyright 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, a higher order compact finite difference solution procedure has been proposed for the steady two-dimensional convection-diffusion equation on non-uniform orthogonal Cartesian grids involving no transformation from the physical space to the computational space.
Abstract: A higher order compact (HOC) finite difference solution procedure has been proposed for the steady two-dimensional (2D) convection–diffusion equation on non-uniform orthogonal Cartesian grids involving no transformation from the physical space to the computational space. Effectiveness of the method is seen from the fact that for the first time, an HOC algorithm on non-uniform grid has been extended to the Navier–Stokes (N–S) equations. Apart from avoiding usual computational complexities associated with conventional transformation techniques, the method produces very accurate solutions for difficult test cases. Besides including the good features of ordinary HOC schemes, the method has the advantage of better scale resolution with smaller number of grid points, with resultant saving of memory and CPU time. Gain in time however may not be proportional to the decrease in the number of grid points as grid non-uniformity imparts asymmetry to some of the associated matrices which otherwise would have been symmetric. The solution procedure is also highly robust as it computes complex flows such as that in the lid-driven square cavity at high Reynolds numbers (Re), for which no HOC results have so far been seen. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, the passive control of bluff body flows using porous media is investigated by means of the penalization method, which is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour.
Abstract: The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two-dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier-Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control
TL;DR: In this paper, an implicit method is developed for solving the complete 3D Navier-Stokes equations, based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid.
Abstract: An implicit method is developed for solving the complete three-dimensional (3D) Navier–Stokes equations. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. A new top-layer pressure treatment and a partial cell bottom treatment are introduced so that the 3D model is fully non-hydrostatic and is free of any hydrostatic assumption. A domain decomposition method is used to segregate the resulting 3D matrix system into a series of two-dimensional vertical plane problems, for each of which a block tri-diagonal system can be directly solved for the unknown horizontal velocity. Numerical tests including linear standing waves, nonlinear sloshing motions, and progressive wave interactions with uneven bottoms are performed. It is found that the model is capable to simulate accurately a range of free-surface flow problems using a very small number of vertical layers (e.g. two–four layers). The developed model is second-order accuracy in time and space and is unconditionally stable; and it can be effectively used to model 3D surface wave motions. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: The paper starts with a scalar convection–diffusion equation and presents a discretization with the aid of the non‐symmetric variant of DGFEM with interior and boundary penalty terms, and extends the scheme to the system of the Navier–Stokes equations.
Abstract: The paper deals with the use of the discontinuous Galerkin finite element method (DGFEM) for the numerical solution of viscous compressible flows. We start with a scalar convection-diffusion equation and present a discretization with the aid of the non-symmetric variant of DGFEM with interior and boundary penalty terms. We also mention some theoretical results. Then we extend the scheme to the system of the Navier-Stokes equations and discuss the treatment of stabilization terms. Several numerical examples are presented
TL;DR: In this article, the characteristic based split scheme is employed for the solution of three-dimensional incompressible viscous flow problems on unstructured meshes, and several algorithm related issues are dis-cussed.
Abstract: SUMMARY In this paper, the characteristic based split scheme is employed for the solution of three-dimensional incompressible viscousow problems on unstructured meshes Many algorithm related issues are dis- cussed Fully explicit and semi-implicit forms of the scheme are explained and employed in the cal- culation of both isothermal and non-isothermal incompressibleows simulation The extension of the scheme to porous mediumows is also demonstrated with relevant examples Copyright ? 2004 John Wiley & Sons, Ltd
TL;DR: In this paper, the authors extended the pressure-based operator splitting algorithm (PISO) to handle the time-dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation.
Abstract: The interfacial dynamics-based cavitation model, developed in Part-1, is further employed for unsteady flow computations. The pressure-based operator-splitting algorithm (PISO) is extended to handle the time-dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation. Furthermore, the compressibility effect is important for unsteady cavitating flows because in a water-vapour mixture, depending on the composition, the speed of sound inside the cavity can vary by an order of magnitude. The implications of the issue of the speed of the sound are assessed with alternative modelling approaches. Depending on the geometric confinement of the nozzle, compressibility model and cavitation numbers, either auto-oscillation or quasi-steady behaviour is observed. The adverse pressure gradient in the closure region is stronger at the maximum cavity size. One can also observe that the mass transfer process contributes to the cavitation dynamics. Compared to the steady flow computations, the velocity and vapour volume fraction distributions within the cavity are noticeably improved with time-dependent computations
TL;DR: In this paper, an implicit finite difference model in the a coordinate system is developed for non-hydrostatic, two-dimensional vertical plane free-surface flows with uneven bottoms, and the unsteady Navier-Stokes equations and the free surface boundary condition are solved simultaneously in a regular transformed domain using a fully implicit method in two steps.
Abstract: An implicit finite difference model in the a co-ordinate system is developed for non-hydrostatic, two-dimensional vertical plane free-surface flows. To accurately simulate interaction of free-surface flows with uneven bottoms, the unsteady Navier-Stokes equations and the free-surface boundary condition are solved simultaneously in a regular transformed a domain using a fully implicit method in two steps. First, the vertical velocity and pressure are expressed as functions of horizontal velocity. Second, substituting these relationship into the horizontal momentum equation provides a block tri-diagonal matrix system with the unknown of horizontal velocity, which can be solved by a direct matrix solver without iteration. A new treatment of non-hydrostatic pressure condition at the top-layer cell is developed
TL;DR: An efficient full approximation storage (FAS) Multigrid algorithm is used to solve a range of droplet spreading flows modelled as a coupled set of non-linear lubrication equations, revealing how droplets can be made to spread preferentially on substrates owing to an interplay between different topographic and surface wetting characteristics.
Abstract: An efficient full approximation storage (FAS) Multigrid algorithm is used to solve a range of droplet spreading flows modelled as a coupled set of non-linear lubrication equations. The algorithm is fully implicit and has embedded within it an adaptive time-stepping scheme that enables the same to be optimized in a controlled manner subject to a specific error tolerance. The method is first validated against a range of analytical and existing numerical predictions commensurate with droplet spreading and then used to simulate a series of new, three-dimensional flows consisting of droplet motion on substrates containing topographic and wetting heterogeneities. The latter are of particular interest and reveal how droplets can be made to spread preferentially on substrates owing to an interplay between different topographic and surface wetting characteristics. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, an extension of the lattice-Boltzmann method for the numerical simulation of three-dimensional electroosmotic flow problems in porous media is presented. But the simulation is restricted to straight cylindrical capillaries with a non-uniform zeta-potential distribution for ratios of the capillary inner radius to the thickness of the electrical double layer.
Abstract: In this article we are concerned with an extension of the lattice-Boltzmann method for the numerical simulation of three-dimensional electroosmotic flow problems in porous media. Our description is evaluated using simple geometries as those encountered in open-channel microfluidic devices. In particular, we consider electroosmosis in straight cylindrical capillaries with a (non)uniform zeta-potential distribution for ratios of the capillary inner radius to the thickness of the electrical double layer from 10 to 100. The general case of heterogeneous zeta-potential distributions at the surface of a capillary requires solution of the following coupled equations in three dimensions: Navier–Stokes equation for liquid flow, Poisson equation for electrical potential distribution, and the Nernst–Planck equation for distribution of ionic species. The hydrodynamic problem has been treated with high efficiency by code parallelization through the lattice-Boltzmann method. For validation velocity fields were simulated in several microcapillary systems and good agreement with results predicted either theoretically or obtained by alternative numerical methods could be established. Results are also discussed with respect to the use of a slip boundary condition for the velocity field at the surface. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, preconditioned iterative techniques for finite-time solutions of a high-order Boussinesq method for modeling water waves in two horizontal dimensions are investigated.
Abstract: This paper investigates preconditioned iterative techniques for nite di erence solutions of a high-order Boussinesq method for modelling water waves in two horizontal dimensions. The Boussinesq method solves simultaneously for all three components of velocity at an arbitrary z-level, removing any practical limitations based on the relative water depth. High-order nite di erence approximations are shown to be more e cient than low-order approximations (for a given accuracy), despite the additional overhead. The resultant system of equations requires that a sparse, unsymmetric, and often ill-conditioned matrix be solved at each stage evaluation within a simulation. Various preconditioning strategies are investigated, including full factorizations of the linearized matrix, ILU factorizations, a matrix-free (Fourier space) method, and an approximate Schur complement approach. A detailed comparison of the methods is given for both rotational and irrotational formulations, and the strengths and limitations of each are discussed. Mesh-independent convergence is demonstrated with many of the preconditioners for solutions of the irrotational formulation, and solutions using the Fourier space and approximate Schur complement preconditioners are shown to require an overall computational e ort that scales linearly with problem size (for large problems). Calculations on a variable depth problem are also compared to experimental data, highlighting the accuracy of the model. Through combined physical and mathematical insight e ective preconditioned iterative solutions are achieved for the full physical application range of the model. Copyright ? 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors present the numerical methods and models implemented in a computer code named zFlow which is capable of simulating inviscid dense gas flows in complex geometries.
Abstract: The study of the dense gas flows which occur in many technological applications demands for fluid dynamic simulation tools incorporating complex thermodynamic models that are not usually available in commercial software. Moreover, the software mentioned can be used to study very interesting phenomena that usually go under the name of ‘non-classical gasdynamics’, which are theoretically predicted for high molecular weight fluids in the superheated region, close to saturation. This paper presents the numerical methods and models implemented in a computer code named zFlow which is capable of simulating inviscid dense gas flows in complex geometries. A detailed description of the space discretization method used to approximate the Euler equations on unstructured grids and for general equations of state, and a summary of the thermodynamic functions required by the mentioned formulation are also given. The performance of the code is demonstrated by presenting two applications, the calculation of the transonic flow around an airfoil computed with both the ideal gas and a complex equation of state and the simulation of the non-classical phenomena occurring in a supersonic flow between two staggered sinusoidal blades. Non-classical effects are simulated in a supersonic flow of a siloxane using a Peng–Robinson-type equation of state. Siloxanes are a class of substances used as working fluids in organic Rankine cycles turbines. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, the performance of the volume of fluid (VOF) and immersed boundary (IB) methods for multi-fluid dynamics is compared with the simulation of a droplet under static equilibrium as a limiting test case and a dropping droplet rising due to gravity for Re less than or equal to 1000.
Abstract: The volume of fluid (VOF) and immersed boundary (IB) methods are two popular computational techniques for multi-fluid dynamics. To help shed light on the performance of both techniques, we present accuracy assessment, which includes interfacial geometry, detailed and global fluid flow characteristics, and computational robustness. The investigation includes the simulations of a droplet under static equilibrium as a limiting test case and a droplet rising due to gravity for Re less than or equal to 1000. Surface tension force models are key issues in both VOF and IB and alternative treatments are examined resulting in improved solution accuracy. A refined curvature model for VOF is also presented. With the newly developed interfacial treatments incorporated, both IB and VOF perform comparably well for the droplet dynamics under different flow parameters and fluid properties.
TL;DR: In this paper, the Navier-Stokes equations are performed with various transport-equation turbulence models in which corrections are added for nonequilibrium flows for the prediction of shock-induced oscillations over rigid airfoils.
Abstract: The prediction of shock-induced oscillations over transonic rigid airfoils is important for a better understanding of the buffeting phenomenon. The unsteady resolution of the Navier-Stokes equations is performed with various transport-equation turbulence models in which corrections are added for nonequilibrium flows. The lack of numerical efficiency due to the CFL stability condition is circumvented by the use of a wall law approach and a dual time stepping method. Moreover, various numerical schemes are used to try and be independent of the numerical discretization. Comparisons are made with the experimental results obtained for the supercritical RA16SC1 airfoil. They show the interest in using the SST correction or realizability conditions to get correct predictions of the frequency, amplitude and pressure fluctuations over the airfoil.
TL;DR: In this article, a two-dimensional near-incompressible steady lid-driven cavityows (Re = 100-7,500) are simulated using multi-relaxation-time (MRT) model in the parallel lattice Boltzmann BGK Bhatnager-Gross Krook method (LBGK).
Abstract: SUMMARY Two-dimensional near-incompressible steady lid-driven cavityows ( Re = 100-7,500) are simulated using multi-relaxation-time (MRT) model in the parallel lattice Boltzmann BGK Bhatnager-Gross- Krook method (LBGK). Results are compared with those using single-relaxation-time (SRT) model in the LBGK method and previous simulation data using Navier-Stokes equations for the sameow conditions. Eects of variation of relaxation parameters in the MRT model, eects of number of the lattice points, improved computational convergence and reduced spatial oscillations of solution near geometrically singular points in theoweld using LBGK method due to MRT model are highlighted in the study. In summary, lattice Boltzmann method using MRT model introduces much less spatial oscillations near geometrical singular points, which is important for the successful simulation of higher Reynolds numberows. Copyright ? 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, a mesh-free weak-strong (MWS) form was proposed for the Navier-Stokes equations that is non-linear in nature, and the MWS method was then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions.
Abstract: A meshfree weak–strong (MWS) form method has been proposed by the authors' group for linear solid mechanics problems based on a combined weak and strong form of governing equations. This paper formulates the MWS method for the incompressible Navier–Stokes equations that is non-linear in nature. In this method, the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries; the local Petrov–Galerkin weak form is applied only to the nodes on the natural boundaries of the problem domain. The MWS method is then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions. The simulation results are validated by comparing with those of other numerical methods as well as experimental data. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. It works perfectly well for irregular nodes using only local quadrature cells for nodes on the natural boundary, which can be generated without any difficulty. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, a Lagrangian Discontinuous Galerkin-type method was proposed to solve 2Duidows on unstructured meshes by using a basis of Bernstein polynomials of degree m in each triangle.
Abstract: SUMMARY This paper concerns a new Lagrangian Discontinuous Galerkin-type method to solve 2Duidows on unstructured meshes. By using a basis of Bernstein polynomials of degree m in each triangle, we dene a diusion process which ensures positivity and stability of the scheme. The discontinuities of the physical variables at the interfaces between cells are solved with an acoustic Riemann solver. A remeshing/remapping process is performed with a particle method: the remapping is locally conservative and its accuracy can be adapted to the accuracy of the numerical method. Copyright ? 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, a finite-volume volume-of-fluid (VOF) method for simulating viscous free surface flows on dynamically adaptive quadtree grids is described. But the method is computationally inefficient in that it provides relatively fine grid resolution at the gas-liquid interface and coarse grid density in regions where flow variable gradients are small.
Abstract: We describe a finite-volume volume-of-fluid (VOF) method for simulating viscous free surface flows on dynamically adaptive quadtree grids. The scheme is computationally efficient in that it provides relatively fine grid resolution at the gas-liquid interface and coarse grid density in regions where flow variable gradients are small. Special interpolations are used to ensure volume flux conservation where differently sized neighbour cells occur. The numerical model is validated for advection of dyed fluid in unidirectional and rotating flows, and for two-dimensional viscous sloshing in a rectangular tank
TL;DR: The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique and a continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux') is introduced for solving the general form of a parabolic diffusion‐convective equation.
Abstract: We present a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further 'normal flux') is introduced for solving the general form of a parabolic diffusion-convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver
TL;DR: In this paper, the Navier slip condition and BC-free boundary condition are applied to the discretized version of the problem, where the normal vector in the discrete problem is not consistent from the point of view of conservation.
Abstract: Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not assure good approximation of the continuum slip condition in the discrete problem, and non-physical recirculating flow fields may be observed. As a remedy, we consider the Navier slip condition, and more successfully, the so-called BC-free boundary condition.