Solving the Convection-Diffusion Equations via a Multiscale and Discontinuous Galerkin Approach

被引：0

作者：

de Jesus, Eneas Mendes ^{[1
,2
]}

dos Santos, Isaac Pinheiro ^{[2
,3
]}

机构：

[1] Fed Inst Espirito Santo IFES, 660 Augusto Costa de Oliveira St, BR-29285000 Piuma, ES, Brazil

[2] Fed Univ Espirito Santo UFES, Postgrad Program Comp Sci PPGI, Ave Fernando Ferrari 514, BR-29075910 Vitoria, ES, Brazil

[3] Fed Univ Espirito Santo UFES, Dept Appl Math DMA, BR 101,Km 60 Litoraneo, BR-29932540 Mateus, ES, Brazil

来源：

COMPUTATIONAL SCIENCE AND ITS APPLICATIONS-ICCSA 2024, PT I | 2024年 / 14813卷

关键词：

Convection-Diffusion equations; Convection-dominated; Discontinuous Galerkin; Artificial diffusion; Multiscale discontinuous Galerkin method; FINITE-ELEMENT METHODS;

D O I：

10.1007/978-3-031-64605-8_8

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a multiscale and discontinuous Galerkin approach for solving the convection-dominated diffusion problems. The unresolved fine-scales are discretized element-wise using bubble functions. A discontinuous Galerkin discretization is employed in the resolved macro scales. To enhance stability to the numerical formulation, we add a nonlinear artificial diffusion operator inside of the elements, acting on both scales, and an extra stabilization on the interelement edges. Numerical tests demonstrate that the method is stable and accurate in solving transport problems with dominant convection.

引用

页码：112 / 124

页数：13

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