A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes
A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes
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DOI：
10.1515/rjnamm.2009.014
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Danilov;Y. Vassilevski
中科院分区：
文献类型：
--
作者：
A. Danilov;Y. Vassilevski
摘要我们发展了一种新的单调网格中心有限体积法，用于在共形多面体网格上离散扩散方程。该方法基于非线性两点磁链近似。对于具有光滑扩散张量和Dirichlet边界条件的问题，该方法是无插值的。在施加扩散张量跳跃或Neumann边界条件的面上应用自适应插值法。该内插基于物理关系，例如扩散通量的连续性。数值实验验证了算法的二阶收敛速度。
Abstract We have developed a new monotone cell-centered finite volume method for the discretization of diffusion equations on conformal polyhedral meshes. The proposed method is based on a nonlinear two-point flux approximation. For problems with smooth diffusion tensors and Dirichlet boundary conditions the method is interpolation-free. An adaptive interpolation is applied on faces where diffusion tensor jumps or Neumann boundary conditions are imposed. The interpolation is based on physical relationships such as continuity of the diffusion flux. The second-order convergence rate is verified with numerical experiments.