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

Kamel Mohamed; Hanan A. Alkhidhr; Mahmoud A. E. Abdelrahman; Kamel Mohamed; Hanan A. Alkhidhr; Mahmoud A. E. Abdelrahman

doi:10.3934/math.2022979

AIMS Mathematics

2022, Volume 7, Issue 10: 17785-17801. doi: 10.3934/math.2022979

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Research article

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

1.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, New valley University, New Valley, Egypt
3.
Department of Mathematics, College of Science, Qassim University, Buraidah, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 03 April 2022 Revised: 07 July 2022 Accepted: 12 July 2022 Published: 03 August 2022
MSC : 35L65, 35L67, 65M08, 76M12, 76N15, 35Q35

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.
- hyperbolic conservation laws,
- Chaplygin gas model,
- NHRS scheme,
- Riemann problem,
- high order accuracy
Citation: Kamel Mohamed, Hanan A. Alkhidhr, Mahmoud A. E. Abdelrahman. The NHRS scheme for the Chaplygin gas model in one and two dimensions[J]. AIMS Mathematics, 2022, 7(10): 17785-17801. doi: 10.3934/math.2022979

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Abstract

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.

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