About some relevant aspects regarding WENO type schemes on the shock tube problem
Journal Title: INCAS BULLETIN - Year 2019, Vol 11, Issue 2
Abstract
The paper is a continuation of the efficiency and accuracy analysis of different high order numerical schemes previously published by the authors [1-3]. After the analysis of advection equation and the scalar conservation equation for different initial conditions and for different convex and non-convex conservative fluxes, we further investigated the one-dimensional conservation equation. This paper focuses on a new comparison of the behavior of the most known Weighted Essentially Non-Oscillatory (WENO) type numerical schemes for shock tube problem. We consider nine different Riemann Problems. Analytical solutions are provided for almost all different initial Riemann conditions. A third-order TVD Runge–Kutta (TVDRK3) scheme was adopted for advancing the solution in time. The motivation of this assessment is related to filling a gap in the specialized literature characterized by the bias towards presenting only cases favorable to a certain method. Our purpose is to present objectively the capacity of each method for solving one-dimensional conservation law problem. Unfortunately, not all the schemes identify accurately the position of the shocks or rarefaction waves and some of them even do not converge to a solution for different Riemann initial conditions.
Authors and Affiliations
Alina BOGOI, Sterian DANAILA, Dragos ISVORANU
Keywords
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- EP ID EP585116
- DOI 10.13111/2066-8201.2019.11.2.5
- Views 94
- Downloads 0
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