A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes
A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes
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DOI：
10.1016/j.jcp.2010.01.035
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
K. Lipnikov;D. Svyatskiy;Y. Vassilevski
中科院分区：
文献类型：
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作者：
K. Lipnikov;D. Svyatskiy;Y. Vassilevski
提出了一种新的二阶精度单调有限体积（FV）方法来求解定态对流扩散方程。该方法采用非线性近似的扩散和对流通量，并保证解决方案的非负性。扩散通量的无插值近似使用Lipnikov [23]中提出的非线性两点模板。平流通量的近似是基于二阶迎风方法，并采用了专门设计的最小非线性校正。数值实验验证了算法的二阶收敛速度和单调性。
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.