Simulating the Brio model via generalized Rusanov scheme in magnetohydrodynamics

The Brio system is a nonlinear system of conservation laws that is used to analyze plasmas. The current research presents numerical solutions to this model exposed to initial conditions using the generalized Rusanov (G. Rusanov) scheme. This method is made up of predictor and corrector phases. In the predictor step, a control parameter for the scheme’s numerical diffusion is present and is controlled using limiter theory and Riemann invariant. The balance conservation equation is considered via the corrector step. The numerical simulation depict that the suggested G. Rusanov method has a high resolution and gives precise simulations for the Brio model in flow regimes with significant shocks and rarefaction. Finally, the G. Rusanov method can also be used to solve a variety of other nonlinear conservation laws. •Applying the generalized Rusanov scheme for the Brio model in magnetohydrodynamics.•Graphical simulations have been introduced to illustrate the behavior of solutions.•We can implement the generalized Rusanov scheme for solving other conservation laws.