Variational multiscale element free Galerkin method for convection-diffusion-reaction equation with small diffusion

Xiaohua Zhang; Hui Xiang

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Variational multiscale element free Galerkin method for convection-diffusion-reaction equation with small diffusion

机译：小扩散对流扩散反应方程的变分多尺度无元素Galerkin方法

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摘要

This paper presents the variational multiscale element free Galerkin method to solve convection-diffusion-reaction equation. The equation under consideration involves a small diffusivity and a large reaction coefficient, which leads to reaction-convection dominated problem. The variational multiscale element free Galerkin method is derived based on Hughes's variational multiscale formulation and element free Galerkin method, thus it inherits the advantages of variational multiscale and meshless methods, meanwhile, the formulation is free of any user-defined parameters owing to the stabilization parameter arises naturally. In order to investigate the presented method, both steady and unsteady 2D convection-diffusion-reaction problems are considered, and the numerical results illustrate the proposed method has the high accuracy and stability for solving convection-diffusion-reaction equation.

机译：本文提出了变分多尺度无元素Galerkin方法来求解对流扩散反应方程。所考虑的方程涉及较小的扩散率和较大的反应系数，这导致反应对流为主的问题。基于休斯的变分多尺度公式和无单元变分Galerkin方法推导了变分多尺度无因Galerkin方法，因此它继承了变分多尺度和无网格方法的优点，同时由于稳定参数，该表达式不包含任何用户定义的参数自然地出现。为了研究该方法，同时考虑了稳态和非稳态二维对流扩散反应问题，数值结果表明，该方法具有较高的精度和稳定性，能够求解对流扩散反应方程。

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来源
《Engineering analysis with boundary elements》 |2014年第9期|85-92|共8页
作者
Xiaohua Zhang; Hui Xiang;
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作者单位

College of Science, China Three Goeges University, Yichang 443002, China;

College of Science, China Three Goeges University, Yichang 443002, China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Variational multiscale method; Convection-diffusion-reaction equation; Meshless method;

机译：变分多尺度方法;对流扩散反应方程;无网格法;

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2. Variational Multiscale Finite-Element Methods for a Nonlinear Convection-Diffusion-Reaction Equation [J] . Zhelnin M. S., Kostina A. A., Plekhov O. A. Journal of Applied Mechanics and Technical Physics . 2020,第7期

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Variational multiscale element free Galerkin method for convection-diffusion-reaction equation with small diffusion

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