A Singular Parameterized Finite Volume Method for the Advection-Diffusion Equation in Irregular Geometries
Year: 2019
Author: Chang Yang, Meng Wu
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 579–608
Abstract
Solving the advection-diffusion equation in irregular geometries is of great importance for realistic simulations. To this end, we adopt multi-patch parameterizations to describe irregular geometries. Different from the classical multi-patch parameterization method, $C^1$-continuity is introduced in order to avoid designing interface conditions between adjacent patches. However, singularities of parameterizations can't always be avoided. Thus, in this paper, a finite volume method is proposed based on smooth multi-patch singular parameterizations. It is called a singular parameterized finite volume method. Firstly, we present a numerical scheme for pure advection equation and pure diffusion equation respectively. Secondly, numerical stability results in $L^2$ norm show that the numerical method is not suffered from the singularities. Thirdly, the numerical method has second order accurate in $L^2$ norm. Finally, three numerical tests in different irregular geometries are presented to show efficiency of this numerical method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1807-m2017-0029
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 579–608
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Finite volume method Smooth multi-patch singular parameterizations The advection-diffusion equation Irregular geometries.