A New Finite Volume Predictor-Corrector Scheme for Simulating the Perfect Gas Dynamics Model in Multiple Spatial Dimensions on Unstructured Meshes

This study presents a new well-balanced scheme for solving hyperbolic conservation equations in multiple spatial dimensions on unstructured meshes. This scheme is fast, accurate, and does not require the solution of the Riemann problem during the computational process. It consists of a predictor and corrector steps: the predictor step uses the method of characteristics to reconstruct the numerical flux, while the corrector step recovers the conservation equations using the finite volume formalism. The scheme’s performance is evaluated on a series of test problems for the multi-dimensional Euler equations to test this scheme’s behavior in a compressible medium through different situations presented in the literature.