Year: 2021
Author: Bassou Khouya, Mofdi El-Amrani, Mohammed Seaid
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 503–526
Abstract
We present an efficient Galerkin-characteristic finite element method for the numerical solution of convection-diffusion problems in three space dimensions. The modified method of characteristics is used to discretize the convective term in a finite element framework. Different types of finite elements are implemented on three-dimensional unstructured meshes. To allocate the departure points we consider an efficient search-locate algorithm for three-dimensional domains. The crucial step of interpolation in the convection step is carried out using the basis functions of the tetrahedron element where the departure point is located. The resulting semi-discretized system is then solved using an implicit time-stepping scheme. The combined method is unconditionally stable such as no Courant-Friedrichs-Lewy condition is required for the selection of time steps in the simulations. The performance of the proposed Galerkin-characteristic finite element method is verified for the transport of a Gaussian sphere in a three-dimensional rotational flow. We also apply the method for simulation of a transport problem in a three-dimensional pipeline flow. In these test problems, the method demonstrates its ability to accurately capture the three-dimensional transport features.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0105
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 3 : pp. 503–526
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Three-dimensional convection-diffusion equations Galerkin-characteristic method finite elements unstructured grids convection-dominated problems.
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