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://doi.org/10.4208/jcm.1807-m2017-0029
UR - https://global-sci.org/intro/article_detail/jcm/13036.html
KW - Finite volume method, Smooth multi-patch singular parameterizations, The advection-diffusion equation, Irregular geometries.
AB - <p style="text-align: justify;">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&#39;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.</p>