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On Exact Conservation for the Euler Equations with Complex Equations of State

Communications in Computational Physics 2010年第10期8卷 995-1015页

作者： J.W.Banks Center for Applied Scientific Computing Lawrence Livermore National LaboratoryLivermoreCA 94551USA

Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near *** is true in that convergent conservative approximations converge to weak solutions and thus have the correct shock ***,correct shock location results from any discretization whose violation of conservation approaches zero as the mesh is *** we investigate the case of the Euler equations for a single gas using the Jones-Wilkins-Lee(JWL)equation of *** show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure ***,we demonstrate that under certain conditions,a quasi-conservative method can exhibit higher rates of convergence near shocks than a strictly conservative counterpart of the same formal order.

关键词： Euler equations complex EOS JWL EOS godunov methods

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A Hybrid Numerical Method to Cure Numerical Shock Instability

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Communications in Computational Physics 2010年第10期8卷 1264-1271页

作者： Hao Wu Longjun Shen Zhijun Shen Institute of Applied Physics and Computational Mathematics BeijingP.O.Box 8009100088China

In this note,we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler *** idea of this method is to combine a”full-wave”Riemann solver and a”less-wave”Riemann solver,which uses a special modified weight based on the difference in velocity *** is also found that such blending does not need to be implemented in all equations of the Euler *** point out that the proposed method is easily extended to other”full-wave”fluxes that suffer from shock *** benchmark problems are presented to validate the proposed method.

关键词： godunov methods numerical shock instability carbuncle phenomenon

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A Stability Analysis of Hybrid Schemes to Cure Shock Instability

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Communications in Computational Physics 2014年第5期15卷 1320-1342页

作者： Zhijun Shen Wei Yan Guangwei Yuan National Key Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China Center for Applied Physics and Technology HEDPSPeking UniversityBeijing 100871China.

The carbuncle phenomenon has been regarded as a spurious solution produced by most of contact-preserving *** hybrid method of combining high resolution flux with more dissipative solver is an attractive attempt to cure this kind of non-physical *** this paper,a matrix-based stability analysis for 2-D Euler equations is performed to explore the cause of instability of numerical *** combining the Roe with HLL flux in different directions and different flux components,we give an interesting explanation to the linear numerical *** on such analysis,some hybrid schemes are compared to illustrate different mechanisms in controlling shock *** experiments are presented to verify our analysis *** conclusion is that the scheme of restricting directly instability source is more stable than other hybrid schemes.

关键词： godunov methods numerical shock instability hybrid scheme.

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