We consider a nonlinear finite volume (FV) scheme for stationary diffusion equation. We prove that the scheme is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The scheme is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients.

Two alternative approaches to the solution of discrete ordinate transport are considered in the context of general unstructured grids. The more traditional approach considered is the solution of a lower triangular system of equations for the spatial intensity distribution. Alternatively, the iterative solution of the system of equations arising from a more general diierencing stencil is also co...

For a large class of physical simulations with relatively simple geometries, unstructured octree-based hexahedral meshes provide a good compromise between adaptivity and simplicity. However, generating unstructured hexahedral meshes with over 1 billion elements remains a challenging task. We propose a database approach to solve this problem. Instead of merely storing generated meshes into conve...

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to da...

in this research, numerical simulation of a symmetric impact of a 2-d wedge, considering dynamic equations in two-phase flow is taken into account. the two-phase flow around the wedge is solved based on finite volume method and volume of fluid (vof) scheme. the dynamic mesh model is used to simulate dynamic motion of the wedge, thereby the effects of different dynamic meshes in both structured ...

A multigrid algorithm is combined with an upwind scheme for solving the twodimensional Reynolds-averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe’s flux-splitting scheme...

In this research, numerical simulation of a symmetric impact of a 2-D wedge, considering dynamic equations in two-phase flow is taken into account. The two-phase flow around the wedge is solved based on finite volume method and volume of fluid (VOF) scheme. The dynamic mesh model is used to simulate dynamic motion of the wedge, thereby the effects of different dynamic meshes in both structured ...