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

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 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.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).