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

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.