局部间断Petrov-Galerkin方法在大气污染模型中的应用

doi:10.19596/j.cnki.1001-246x.8192

计算物理 ›› 2021, Vol. 38 ›› Issue (2): 171-182.DOI: 10.19596/j.cnki.1001-246x.8192

局部间断Petrov-Galerkin方法在大气污染模型中的应用

张欣¹, 赵国忠², 李宏¹

1. 内蒙古大学数学科学学院, 内蒙古呼和浩特 010000;
2. 包头师范学院数学科学学院, 内蒙古包头 014030

收稿日期:2020-01-02 修回日期:2020-03-04 发布日期:2021-09-29
通讯作者: 赵国忠,E-mail:zhaoguozhongbttc@sina.com;李宏,E-mail:smslh@imu.edu.cn
作者简介:张欣(1996-),女,硕士,从事偏微分方程数值解研究
基金资助:
国家自然科学基金（11761054，11261035）、内蒙古自治区高等学校青年科技英才项目（NJYT-15-A07）、内蒙古自然科学基金（2015MS0108，2012MS0102）及内蒙古高等学校科学研究项目（NJZZ12198，NJZZ16234，NJZZ16235）资助

Local Discontinuous Petrov-Galerkin Method in Air Pollution Model

ZHANG Xin¹, ZHAO Guozhong², LI Hong¹

1. Faculty of Mathematics, Inner Mongolia University, Hohhot, Inner Mongolia 010000, China;
2. Faculty of Mathematics, Baotou Teachers' College, Baotou, Inner Mongolia 014030, China

Received:2020-01-02 Revised:2020-03-04 Published:2021-09-29

摘要/Abstract

摘要： 构造数值模拟两类大气污染模型的局部间断Petrov-Galerkin方法。首先通过变量代换将大气污染模型方程转化为与之等价的一阶微分方程组，再利用间断Petrov-Galerkin方法求解微分方程组。该方法既可以选取不同的检验函数和试探函数空间，又可以保持间断Petrov-Galerkin方法的优势。同局部间断有限元方法相比，该方法的计算公式较为简便，数值算例表明该方法具有三阶精度。与有限体积元方法相比，该方法具有较小的误差。本算法可为大气污染模型的数值模拟提供实用工具。

关键词: 局部间断Petrov-Galerkin方法, 大气污染模型, TVD Runge-Kutta方法, 数值流通量

Abstract: A local discontinuous Petrov-Galerkin method for numerical simulation of two kinds of air pollution models is constructed. Firstly, air pollution model equations are transformed into equivalent first-order differential equations with variable substitution. Secondly, discontinuous Petrov-Galerkin method is used to solve the differential equations. The method can choose different test function and trial function space, and maintains advantages of the intermittent Petrov-Galerkin method. Compared with local discontinuous finite element method, calculation formula of the method is simpler. Numerical examples show that the method has third-order accuracy and less error than the finite volume method. The algorithm provides a practical tool for numerical simulation of air pollution models.

Key words: local discontinuous Petrov-Galerkin method, air pollution model, TVD Runge-Kutta method, numerical flux

中图分类号:

O241.82

张欣, 赵国忠, 李宏. 局部间断Petrov-Galerkin方法在大气污染模型中的应用[J]. 计算物理, 2021, 38(2): 171-182.

ZHANG Xin, ZHAO Guozhong, LI Hong. Local Discontinuous Petrov-Galerkin Method in Air Pollution Model[J]. Chinese Journal of Computational Physics, 2021, 38(2): 171-182.

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局部间断Petrov-Galerkin方法在大气污染模型中的应用

Local Discontinuous Petrov-Galerkin Method in Air Pollution Model

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