The NHRS scheme for the Chaplygin gas model in one and two dimensions

AIMS Mathematics

article

Kamel Mohamed¹  Hanan A. Alkhidhr³  Mahmoud A. E. Abdelrahman¹ 

[1] Department of Mathematics, College of Science, Taibah University;Department of Mathematics, Faculty of Science, New valley University;Department of Mathematics, College of Science, Qassim University;Department of Mathematics, Faculty of Science, Mansoura University

关键词: hyperbolic conservation laws;    Chaplygin gas model;    NHRS scheme;    Riemann problem;    high order accuracy;   

DOI  :  10.3934/math.2022979

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

The main motive of this work is to introduce a numerical investigation for the one and two-dimensional (1D/2D) Chaplygin gas model. Namely, we developed the non homogeneous Riemann solver (NHRS) method to solve these models. After discussing the Chaplygin gas models and the numerical scheme, various 1D and 2D test problems are introduced. In order to complete the numerical investigation in a completely unified way, Rusanov scheme, modified Lax-Friedrichs and analytical solution are compared with NHRS scheme in 1D case. The acquired results clarify the high resolution of the NHRS technique. The NHRS technique is efficacious and robust. Finally, our study displays that the NHRS scheme is a very powerful tool to solve many other models arising in applied science.

【 授权许可】

CC BY