@Article{JCM-37-5,
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 = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1807-m2017-0029},
url = {https://global-sci.com/article/84432/a-singular-parameterized-finite-volume-method-for-the-advection-diffusion-equation-in-irregular-geometries}
}