A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2017, Vol. 34 ›› Issue (3): 294-308.

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A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates

ZHAO Guozhong¹, YU Xijun², GUO Huaimin¹

1. Faculty of Mathematics, Baotou Teachers' College, Baotou 014030, China;
2. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2016-03-18 Revised:2016-06-15 Online:2017-05-25 Published:2017-05-25
Supported by:
National Natural Science Foundation of China (11261035,11571002), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-15-A07), Natural Science Foundation of Inner Mongolia Autonomous Region, China (2015MS0108, 2012MS0102), Science Research Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region, China (NJZZ12198), Science and Technology Development Foundation of CAEP (2015B0101021) and Defense Industrial Technology Development Program(B1520133015)

Abstract

Abstract: A cell-centered scheme is constructed for two-dimensional gas dynamics equations in Lagrangian coordinates on rectangular grids. Spacial discretizations are accomplished by control volume discontinuous Petrov-Galerkin method and temporal discretization is accomplished by second order total variation diminishing Runge-Kutta method. A limiter is used to maintain stability and non-oscillatory property of Runge-Kutta control volume (RKCV) method. The method preserves local conservation of physical variables. Compared with Runge-Kutta discontinuous Galerkin (RKDG) method, computational formula of RKCV method is simpler since it contains no volume quadrature in RKDG method. Numerical examples are given to demonstrate reliability and efficiency of the algorithm.

Key words: compressible gas dynamic equations, RKCV discontinuous finite element method, Lagrangian coordinate

CLC Number:

O241.82

ZHAO Guozhong, YU Xijun, GUO Huaimin. A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(3): 294-308.

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A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates

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