Developing Numerical Fluxes with New Sonic Fix for MHD Equations

This research focuses on advanced solutions for hyperbolic equation systems using upwind, second-order accurate fluxes integrated with an innovative sonic fix. This sonic fix is based on physical principles, ensuring accurate decay rates for sonic gradients. Additionally, we explore the effects of source terms on flux limiters and introduce an enhanced approach to handling magneto-hydrodynamic (MHD) equations that addresses divergence issues with a built-in divergence wave. Extensive testing shows that this methodology provides robust, precise, and entropy-consistent results, delivering sharp contact discontinuities and shock resolution without oscillations or errors.