A least squares based diamond scheme for anisotropic diffusion problems on polygonal meshes,International Journal for Numerical Methods in Fluids

当前位置： X-MOL 学术 › Int. J. Numer. Methods Fluids › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

A least squares based diamond scheme for anisotropic diffusion problems on polygonal meshes
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-07-10 , DOI: 10.1002/fld.5031
Cheng Dong _{1,

2} , Tong Kang _{1,

2}

Affiliation

We present a new least squares based diamond scheme for anisotropic diffusion problems on polygonal meshes. This scheme introduces both cell-centered unknowns and vertex unknowns. The vertex unknowns are intermediate ones and are expressed as linear combinations with the surrounding cell-centered unknowns by a new vertex interpolation algorithm which is also derived in least squares approach. Both the new scheme and the vertex interpolation algorithm are applicable to diffusion problems with arbitrary diffusion tensors and do not depend on the location of discontinuity. Benefitting from the flexibility of least squares approach, the new scheme and vertex interpolation algorithm can also be extended to 3D cases naturally. The new scheme and vertex interpolation algorithm are linearity-preserving under given assumptions and the numerical results show that they maintain nearly optimal convergence rates for both

L^{2}

error and

H^{1}

error in general cases. More interesting is that a very robust performance of the new vertex interpolation algorithm on random meshes compared with the algorithm LPEW2 is found from the numerical tests.

中文翻译：

多边形网格上各向异性扩散问题的基于最小二乘法的菱形方案

我们针对多边形网格上的各向异性扩散问题提出了一种新的基于最小二乘法的菱形方案。该方案引入了以单元为中心的未知数和顶点未知数。顶点未知数是中间未知数，并通过新的顶点插值算法表示为与周围以单元格为中心的未知数的线性组合，该算法也是在最小二乘法中推导出来的。新方案和顶点插值算法都适用于具有任意扩散张量的扩散问题，并且不依赖于不连续的位置。受益于最小二乘法的灵活性，新方案和顶点插值算法也可以自然地扩展到 3D 情况。