A modified version of the finite volume scheme for numerical simulation of 1D non-ideal isentropic magnetogasdynamics

Reem Alotaibi; H. G. Abdelwahed; Kamel Mohamed; Mahmoud A. E. Abdelrahman; Reem Alotaibi; H. G. Abdelwahed; Kamel Mohamed; Mahmoud A. E. Abdelrahman

doi:10.3934/math.2026061

AIMS Mathematics

2026, Volume 11, Issue 1: 1449-1462. doi: 10.3934/math.2026061

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A modified version of the finite volume scheme for numerical simulation of 1D non-ideal isentropic magnetogasdynamics

1.
Department of Physics, College of Science and Humanities, Al-Kharj, Prince Sattam bin Abdulaziz University, Al- Kharj11942, Saudi Arabia
2.
Department of Mathematics and computer sciences, Faculty of Science, New Valley University, New Valley, Egypt
3.
Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt

Received: 25 August 2025 Revised: 06 December 2025 Accepted: 12 December 2025 Published: 19 January 2026
MSC : 35L65, 35Q35, 65M08, 76N15, 76W05

Magnetogasdynamics (MGD) is an interdisciplinary area of study that investigates the properties and behavior of electrically conductive gases, including plasmas and ionized fluids, when subjected to magnetic and electric fields. MGD is essential for simulating how electromagnetic fields affect electrically conducting gases, especially in flow regimes with high temperatures and speeds. This article examines a one-dimensional non-ideal isentropic magnetogasdynamic. We offer a modified version of finite volume (MVFV) method for the numerical analysis of this model. This approach represents an improved iteration of the Rusanov scheme, a widely utilized finite volume method for the numerical resolution of hyperbolic systems of conservation laws, particularly in the fields of MGD and fluid dynamics. The MVFV method is structured into two distinct phases: the predictor phase and the corrector phase. The predictor relies on the control parameter, which is responsible for the numerical diffusion of this method. The second phase reinstates the balance conservation equation. The MVFV technique's results are compared to the exact solution and the Harten–Lax–van Leer (HLL) approach in the numerical simulation. The findings validate the reliability of MGD models in effectively representing critical nonlinear phenomena and establish a foundation for forthcoming numerical simulations and experimental verification.
- conservation laws,
- non-ideal isentropic MGD,
- MVFV scheme,
- HLL scheme
Citation: Reem Alotaibi, H. G. Abdelwahed, Kamel Mohamed, Mahmoud A. E. Abdelrahman. A modified version of the finite volume scheme for numerical simulation of 1D non-ideal isentropic magnetogasdynamics[J]. AIMS Mathematics, 2026, 11(1): 1449-1462. doi: 10.3934/math.2026061

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Abstract

Magnetogasdynamics (MGD) is an interdisciplinary area of study that investigates the properties and behavior of electrically conductive gases, including plasmas and ionized fluids, when subjected to magnetic and electric fields. MGD is essential for simulating how electromagnetic fields affect electrically conducting gases, especially in flow regimes with high temperatures and speeds. This article examines a one-dimensional non-ideal isentropic magnetogasdynamic. We offer a modified version of finite volume (MVFV) method for the numerical analysis of this model. This approach represents an improved iteration of the Rusanov scheme, a widely utilized finite volume method for the numerical resolution of hyperbolic systems of conservation laws, particularly in the fields of MGD and fluid dynamics. The MVFV method is structured into two distinct phases: the predictor phase and the corrector phase. The predictor relies on the control parameter, which is responsible for the numerical diffusion of this method. The second phase reinstates the balance conservation equation. The MVFV technique's results are compared to the exact solution and the Harten–Lax–van Leer (HLL) approach in the numerical simulation. The findings validate the reliability of MGD models in effectively representing critical nonlinear phenomena and establish a foundation for forthcoming numerical simulations and experimental verification.

References

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