A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities
A multiscale model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities
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DOI：
10.1016/j.jcp.2019.109177
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
Raaghav Ramani;S. Shkoller
中科院分区：
文献类型：
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作者：
Raaghav Ramani;S. Shkoller
我们开发了一种新颖的多尺度界面运动模型，用于二维、无粘性、带涡量的可压缩流的瑞利-泰勒不稳定性 (RTI) 和 Richtmyer-Meshkov 不稳定性 (RMI)，这产生了一种快速运行的数值算法，可以在定性和定量上产生与解析的气体动力学代码相似的结果，同时运行速度（时间）大约快两个数量级。我们的多尺度模型建立在速度场 u= v+ w 的新的可压缩-不可压缩分解的基础上。速度的不可压缩分量 w 也是无旋的，并且使用不可压缩欧拉方程的 Birkhoff-Rott 奇异积分公式的新渐近模型进行求解，从而将问题减少到一个空间维度。这种渐近模型称为高阶 z 模型，是利用渐近参数中的小非局域性导出的，允许界面翻转和卷起，并对描述涡度振幅演化的方程进行了显着简化。速度的不可压缩分量 w 控制界面的小尺度结构，并且可以在精细网格上有效求解。同时，速度 v 的可压缩分量在接触不连续点附近保持连续，并且可以在相对粗糙的网格上计算，同时从 w 接收子网格尺度信息。我们首先通过与经典 RTI 实验以及全点涡模拟进行比较来验证不可压缩高阶 z 模型。然后，我们考虑带有涡量的可压缩流多尺度模型的 RTI 和 RMI 问题，并与我们的高分辨率气体动力学解决方案表现出极好的一致性。
We develop a novel multiscale model of interface motion for the Rayleigh-Taylor instability (RTI) and Richtmyer-Meshkov instability (RMI) for two-dimensional, inviscid, compressible flows with vorticity, which yields a fast-running numerical algorithm that produces both qualitatively and quantitatively similar results to a resolved gas dynamics code, while running approximately two orders of magnitude (in time) faster. Our multiscale model is founded upon a new compressible-incompressible decomposition of the velocity field u= v+ w. The incompressible component w of the velocity is also irrotational and is solved using a new asymptotic model of the Birkhoff-Rott singular integral formulation of the incompressible Euler equations, which reduces the problem to one spatial dimension. This asymptotic model, called the higher-order z-model, is derived using small nonlocality in the asymptotic parameter, allows for interface turn-over and roll-up, and yields a significant simplification for the equation describing the evolution of the amplitude of vorticity. This incompressible component w of the velocity controls the small scale structures of the interface and can be solved efficiently on fine grids. Meanwhile, the compressible component of the velocity v remains continuous near contact discontinuities and can be computed on relatively coarse grids, while receiving subgrid scale information from w. We first validate the incompressible higher-order z-model by comparison with classical RTI experiments as well as full point vortex simulations. We then consider both the RTI and the RMI problems for our multiscale model of compressible flow with vorticity, and show excellent agreement with our high-resolution gas dynamics solutions.