含Goddom SPH的Kelvin-Helmholtz不稳定性
Kelvin-Helmholtz instabilities with Godunov SPH
摘要：
本文用Inutsuka（2002）发展的粒子方法（Goddom SPH）对两种不同密度层中Kelvin-Helmholtz不稳定性的非线性发展进行了数值模拟。即使在高密度对比下，Goddom SPH也可以描述Kelvin-Helmholtz不稳定性，而标准SPH显示在密度梯度上不存在不稳定性（Agertz等人，2007）。还进行了稠密液滴与热环境介质的相互作用。Goddom SPH描述了由于Rayleigh-Taylor、Richtmyer-Meshkov和Kelvin-Helmholtz不稳定性的组合而导致的指状物的形成和演化。斑点测试结果与基于网格的代码的结果吻合良好。指出标准SPH中密度梯度处理不准确是不存在不稳定性的直接原因。即使在压力平衡下，密度梯度处也会产生一个非物理力，将粒子从初始密度不连续处排斥出去。因此，初始扰动衰减，并且在不连续处形成间隙。从数值格式的一致性角度研究了非物理力的作用。与标准SPH相反，Goddom SPH的动量方程不使用粒子近似，而是由核卷积或新的拉格朗日函数导出。在Goddom SPH中使用的新的拉格朗日函数更类似于连续介质的真实拉格朗日函数。Goddom SPH的动量方程具有更好的线性一致性，因此在高密度对比下，非物理力比标准SPH大大减少。
英文摘要：
Numerical simulations for the non-linear development of Kelvin-Helmholtz instability in two different density layers have been performed with the particle-based method (Godunov SPH) developed by Inutsuka (2002). The Godunov SPH can describe the Kelvin-Helmholtz instability even with a high density contrast, while the standard SPH shows the absence of the instability across a density gradient (Agertz et al. 2007). The interaction of a dense blob with a hot ambient medium has been performed also. The Godunov SPH describes the formation and evolution of the fingers due to the combinations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities. The blob test result coincides well with the results of the grid-based codes. An inaccurate handling of a density gradient in the standard SPH has been pointed out as the direct reason of the absence of the instabilities. An unphysical force happens at the density gradient even in a pressure equilibrium, and repulses particles from the initial density discontinuity. Therefore, the initial perturbation damps, and a gap forms at the discontinuity. The unphysical force has been studied in terms of the consistency of a numerical scheme. Contrary to the standard SPH, the momentum equation of the Godunov SPH doesnt use the particle approximation, and has been derived from the kernel convolution or a new Lagrangian function. The new Lagrangian function used in the Godunov SPH is more analogous to the real Lagrangian function for continuum. The momentum equation of the Godunov SPH has much better linear consistency, so the unphysical force is greatly reduced compared to the standard SPH in a high density contrast.
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