Numerical discrepancies of using a nonconservative formulation of the compressible gas flow model

Ferdinand E. Uilhoorn
2019 Journal of Applied Mathematics and Computational Mechanics  
In this article, we investigated the shock phenomenon in gas pipeline systems. We particularly address the numerical discrepancies introduced when using a primitive variable-based formulation of the compressible gas flow model. For the analysis, we compared two different schemes, namely, van Leer's second-order Monotonic Upstream-centered Scheme for Conservation Laws scheme (TVD-MUSCL) together with Roe's superbee slope limiter and the fifth-order accurate finite volume weighted essentially
more » ... ted essentially non-oscillatory scheme (WENO5-Z). For the numerical flux, we implemented the Rusanov solver. The time stepping was done with a strong stability preserving Runge-Kutta method. The method of manufactured solutions was used to verify the code accuracy. Based on a series of numerical experiments, we showed that the local errors become more visible if we use the WENO5-Z reconstruction. MSC 2010: 74H15, 76N15
doi:10.17512/jamcm.2019.4.10 fatcat:v2nbb5duprffxe47fs6qn66wpq