2024/01/08 by Mária Lukáčová-Medviďová, Lukacova-Medvidova, Maria, Yuhuan Yuan +1 · 1 citation
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2401.03714
openalex publication_date 2024/01/08 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
In this paper we study the convergence of a second order finite volume approximation of the scalar conservation law. This scheme is based on the generalized Riemann problem (GRP) solver. We firstly investigate the stability of the GRP scheme and find that it might be entropy unstable when the shock wave is generated. By adding an artificial viscosity we propose a new stabilized GRP scheme. Under the assumption that numerical solutions are uniformly bounded, we prove consistency and convergence of this new GRP method.