Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
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单网格和双网格上物理兼容的离散化技术，应用于体积形式的泊松方程
DOI：
10.1016/j.jcp.2013.08.005
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Gerritsma
中科院分区：
文献类型：
--
作者：
A. Palha;P. Rebelo;R. Hiemstra;Jasper J. Kreeft;M. Gerritsma
本文介绍了物理兼容离散化技术的基本概念。该论文明确区分了向量和形式。基于形式和伪形式之间的差异以及两者之间切换的⋆算子，提出了双网格描述和单网格描述。双网格方法类似于交错有限体积方法，而单网格方法与有限元方法非常相似。比较了体积形式的泊松方程的两种方法。通过为 1-形式定义适当加权的内积，这种方法可以很容易地应用于体积形式的各向异性扩散模型。
This paper introduces the basic concepts for physics-compatible discretization techniques. The paper gives a clear distinction between vectors and forms. Based on the difference between forms and pseudo-forms and the ⋆-operator which switches between the two, a dual grid description and a single grid description are presented. The dual grid method resembles a staggered finite volume method, whereas the single grid approach shows a strong resemblance with a finite element method. Both approaches are compared for the Poisson equation for volume forms. By defining a suitably weighted inner product for 1-forms this approach can readily be applied to anisotropic diffusion models for volume forms.