Conservative interpolation between unstructured meshes via supermesh construction
Conservative interpolation between unstructured meshes via supermesh construction
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DOI：
10.1016/j.cma.2009.03.004
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发表时间：
2009-07
影响因子：
7.2
通讯作者：
P. Farrell;M. Piggott;C. Pain;G. Gorman;Cristy Wilson
中科院分区：
文献类型：
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作者：
P. Farrell;M. Piggott;C. Pain;G. Gorman;Cristy Wilson
非结构网格的网格自适应性是一个行之有效的和流行的工具，以减少数值模拟的计算成本。非结构化网格在网格自适应中通常是首选的，因为它们在解析模拟特征时允许更大的几何灵活性和任意各向异性。然而，这种网格自适应性具有显著的缺点：由从旧网格到新网格的内插引起的内插误差通常破坏对模拟的物理精度重要的量的守恒（例如，密度、体积分数、示踪剂浓度等）。本文通过构造一个中间超网格，给出了一般非结构网格之间的几种全局守恒插值算子。超网格的构造是通过将问题转化为约束网格化问题的输入来进行的。保守插值算子的性能进行了比较，对插值使用的基础函数。
Mesh adaptivity on unstructured meshes is a proven and popular tool for reducing the computational cost of numerical simulations. Unstructured meshes are often preferred in mesh adaptivity as they allow for greater geometric flexibility and arbitrary anisotropy in resolving simulation features. However, such mesh adaptivity suffers from a significant drawback: the interpolation errors caused by interpolating from the old mesh to the new mesh typically destroys conservation of quantities important to the physical accuracy of the simulation (e.g., density, volume fraction, tracer concentration, etc.). This work presents several globally conservative interpolation operators between general unstructured meshes via the construction of an intermediate supermesh. The construction of the supermesh is performed by transforming the problem to the input to a constrained meshing problem. The performance of the conservative interpolation operators are compared against interpolation using the underlying basis functions.