MIMETIC SCHEMES ON NON-UNIFORM STRUCTURED MESHES
MIMETIC SCHEMES ON NON-UNIFORM STRUCTURED MESHES
复制标题
非均匀结构化网格的模拟方案
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J. Castillo
中科院分区：
文献类型：
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作者：
E. D. Batista;J. Castillo
模拟算子是满足连续守恒律离散形式的近似。提出了一种基于局部变换和使用参考单元集（RSC）的非均匀结构网格上的仿散度和梯度算子的构造方法. RSC不是网格，而是在构建运算符时使用的两个统一元素的集合。该方法已被应用于构造非均匀一维网格上的二阶和四阶梯度算子和散度算子。我们的方法使均匀和非均匀网格的边界算子表达式保持不变，这是一个新的结果，也是我们公式的一个优点。最后，通过求解一个具有Robin边界条件的边界层问题，给出了数值收敛性分析，表明采用自适应网格可以获得最高精度。
Mimetic operators are approximations that satisfy discret e v rsions of continuum conservation laws. We propose a technique for constructing mimetic divergence and gradient operators over non-uniform structured meshes based on the application of local transformations an d the use of a reference set of cells (RSC). The RSC is not a mesh, but a set of two uniform elements that are used whil e the operators are being built. The method has been applied to construct second and fourth order gradient a nd divergence operators over non-uniform 1D meshes. Our approach leaves invariant the boundary operator expres sions for uniform and non-uniform meshes, which is a new result and an advantage of our formulation. Finally, a nu merical convergence analysis is presented by solving a boundary layer like problem with Robin boundary condition s; this shows that we can obtain the highest order of accuracy when implementing adapted meshes.