Volume 37, Issue 5
A Singular Parameterized Finite Volume Method for the Advection-Diffusion Equation in Irregular Geometries

Chang Yang & Meng Wu

J. Comp. Math., 37 (2019), pp. 579-608.

Published online: 2019-03

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  • 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, C1- 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 L2norm show that the numerical method is not suffered from the singularities. Thirdly, the numerical method has second order accurate in L2norm. Finally, three numerical tests in different irregular geometries are presented to show efficiency of this numerical method.

  • Keywords

Finite volume method, Smooth multi-patch singular parameterizations, The advection-diffusion equation, Irregular geometries.

  • AMS Subject Headings

65D17, 65M08, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangchang@hit.edu.cn (Chang Yang)

meng.wu@hfut.edu.cn (Meng Wu)

  • BibTex
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  • TXT
@Article{JCM-37-579, author = {Yang , Chang and Wu , Meng }, title = {A Singular Parameterized Finite Volume Method for the Advection-Diffusion Equation in Irregular Geometries}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {5}, pages = {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, C1- 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 L2norm show that the numerical method is not suffered from the singularities. Thirdly, the numerical method has second order accurate in L2norm. Finally, three numerical tests in different irregular geometries are presented to show efficiency of this numerical method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1807-m2017-0029}, url = {http://global-sci.org/intro/article_detail/jcm/13036.html} }
TY - JOUR T1 - A Singular Parameterized Finite Volume Method for the Advection-Diffusion Equation in Irregular Geometries AU - Yang , Chang AU - Wu , Meng JO - Journal of Computational Mathematics VL - 5 SP - 579 EP - 608 PY - 2019 DA - 2019/03 SN - 37 DO - http://dor.org/10.4208/jcm.1807-m2017-0029 UR - https://global-sci.org/intro/jcm/13036.html KW - Finite volume method, Smooth multi-patch singular parameterizations, The advection-diffusion equation, Irregular geometries. AB -

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, C1- 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 L2norm show that the numerical method is not suffered from the singularities. Thirdly, the numerical method has second order accurate in L2norm. Finally, three numerical tests in different irregular geometries are presented to show efficiency of this numerical method.

Chang Yang & Meng Wu. (2019). A Singular Parameterized Finite Volume Method for the Advection-Diffusion Equation in Irregular Geometries. Journal of Computational Mathematics. 37 (5). 579-608. doi:10.4208/jcm.1807-m2017-0029
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