A SING ULAR PARAM ETERIZED FINITE VOLUME METHOD FOR THE ADVECTION-DIFFUSION EQUATION IN IRREGULAR GEOMETRIES  

作　　者：Chang Yang Meng Wu 

机构地区：[1]Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China [2]School of Mathematics,Hefei University of Technology,Hefei 230026,China

出　　处：《Journal of Computational Mathematics》2019年第5期579-608,共30页计算数学（英文）

基　　金：The authors are grateful to the anonymous reviewers for their useful comments and suggestions;The authors are supported by the NSF of China (No. 11601114, No.11401138);the Anhui Provincial Natural Science Foundation (No. 1608085QA14).

摘　　要：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 L2 norm show that the numerical method is not suffered from the singularities. Thirdly, the numerical method has second order accurate in L2 norm. Finally, three numerical tests in different irregular geometries are presented to show efficiency of this numerical method.

关 键 词：Finite volume method Smooth multi-patch SINGULAR PARAMETERIZATIONS The ADVECTION-DIFFUSION equation IRREGULAR GEOMETRIES 

分 类 号：O1[理学—数学]