A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes

被引：89
|
作者：
Lipnikov, K. [1 ]
Svyatskiy, D. [1 ]
Vassilevski, Y. [2 ]
机构：
[1] Los Alamos Natl Lab, Div Theoret, Appl Math & Plasma Phys Grp, Los Alamos, NM 87545 USA
[2] Russian Acad Sci, Inst Numer Math, Moscow 119333, Russia
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2010年 / 229卷 / 11期
关键词：
Advection-diffusion equation; Finite volume method; Discrete maximum principle; Monotone method; Unstructured mesh; Polygonal mesh; DISCRETE MAXIMUM PRINCIPLE; TETRAHEDRAL MESHES; CONVECTION; SCHEMES; LIMITERS; GRIDS;
D O I：
10.1016/j.jcp.2010.01.035
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We present a new second-order accurate monotone finite volume (FV) method for the steady-state advection-diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes and guarantees solution non-negativity. The interpolation-free approximation of the diffusive flux uses the nonlinear two-point stencil proposed in Lipnikov [23]. Approximation of the advective flux is based on the second-order upwind method with a specially designed minimal nonlinear correction. The second-order convergence rate and monotonicity are verified with numerical experiments. Published by Elsevier Inc.
引用
收藏
页码：4017 / 4032
页数：16
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