A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes

Authors:
Zhiqiang Sheng;Guangwei Yuan
Affiliations:
szqdxy@163.com;yuan_guangwei@iapcm.ac.cn
Venue:
SIAM Journal on Scientific Computing
Year:
2008

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Abstract

A nine point scheme is presented for discretizing diffusion operators on distorted quadrilateral meshes. The advantage of this method is that highly distorted meshes can be used without the numerical results being altered remarkably, and it treats material discontinuities rigorously and offers an explicit expression for the face-centered flux; moreover, it has only the cell-centered unknowns. We prove that the method is stable and has first-order convergence on distorted meshes. Numerical experiments show that the method has second-order or nearly second-order accuracy on distorted meshes.