Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes
Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes
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DOI：
10.1016/j.compfluid.2007.07.023
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发表时间：
2009
影响因子：
2.8
通讯作者：
V. Caselles;R. Donat;G. Haro
中科院分区：
文献类型：
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作者：
V. Caselles;R. Donat;G. Haro
我们给出了Fedkiw等人[Fedkiw RP，Merriman B，Donat R，Osher S.守恒律方程组的倒数第二个格式：带Marquina通量分裂的有限差分ENO。In：Hafez M，editor.偏微分方程数值解的进展，阿尔卡雄，法国; 1998年7月]，浅水系统。我们表明，在单元格界面使用两个不同的雅可比行列式会阻止该方案满足精确的C-性质[Bermúdez A，Vázquez ME.带源项的双曲守恒律的迎风方法。Comput Fluids 1994;23（8）：1049-71]，而高阶格式满足近似C性质。在Marquina的通量分裂公式中使用单个Jacobian导致满足精确C-性质的数值方案，因此我们提出了一种组合技术，当两个相邻状态不接近时使用Marquina的双侧分解，否则使用单个分解。最后，我们提出了一个特殊的治疗在湿/干前线和干床生成的情况。
We present an extension of Marquina’s flux formula, as introduced in Fedkiw et al. [Fedkiw RP, Merriman B, Donat R, Osher S. The penultimate scheme for systems of conservation laws: finite difference ENO with Marquina’s flux splitting. In: Hafez M, editor. Progress in numerical solutions of partial differential equations, Arcachon, France; July 1998], for the shallow water system. We show that the use of two different Jacobians at cell interfaces prevents the scheme from satisfying the exact C-property [Bermúdez A, Vázquez ME. Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 1994;23(8):1049–71] while the approximate C-property is satisfied for higher order versions of the scheme. The use of a single Jacobian in Marquina’s flux splitting formula leads to a numerical scheme satisfying the exact C-property, hence we propose a combined technique that uses Marquina’s two sided decomposition when the two adjacent states are not close and a single decomposition otherwise. Finally, we propose a special treatment at wet/dry fronts and situations of dry bed generation.