Anti-diffusion interface sharpening technique for two-phase compressible flow simulations
Anti-diffusion interface sharpening technique for two-phase compressible flow simulations
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DOI：
10.1016/j.jcp.2012.02.013
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
K. K. So-K.;Xiangyu Y. Hu;N. Adams
中科院分区：
文献类型：
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作者：
K. K. So-K.;Xiangyu Y. Hu;N. Adams
本文提出了一种基于流体体积法的两相可压缩流模拟界面锐化技术。锐化两流体界面的思想是提供一种校正算法，该算法可以在每个时间步长后对体积分数场进行后处理。为此，求解一个反扩散方程，即具有正扩散系数的扩散方程，以抵消由底层VOF离散化引起的数值扩散。采用特定的离散化方法，保证了反扩散方程的数值稳定性和体积分数有界性。该方法不需要进行界面重构和界面法向计算。为了保证变量的一致性，所有流动变量都采用锐化的体积分数场进行更新，并且相质量、动量和能量的更新是保守的。基于理想气体方程的激波管和激波泡相互作用以及基于mie - grisen方程的激波接触问题的数值结果表明，界面分辨率有所提高。大尺度界面结构与参考结果吻合较好，随着网格分辨率的提高，更精细的小尺度界面结构得到了一致的恢复。与基于AMR算法的参考高网格分辨率数值结果相比，对于涉及不同理想气体的激波气泡相互作用，可以可靠地恢复由richmyer - meshkov不稳定性和Kelvin-Helmholtz不稳定性引起的界面卷起现象。
In this paper we propose an interface sharpening technique for two-phase compressible-flow simulations based on volume-of-fluid methods. The idea of sharpening the two-fluid interface is to provide a correction algorithm which can be applied as post-processing to the volume-fraction field after each time step. For this purpose an anti-diffusion equation, i.e. a diffusion equation with a positive diffusion coefficient, is solved to counter-act the numerical diffusion resulting from the underlying VOF discretization. The numerical stability and volume-fraction boundedness in solving the anti-diffusion equation are ensured by a specified discretization scheme. No interface reconstruction and interface normal calculation are required in this method. All flow variables are updated with the sharpened volume-fraction field for ensuring the consistency of the variables, and the update of the phase mass, momentum and energy is conservative. Numerical results for shock-tube and shock-bubble interactions based on the ideal-gas EOS and shock contact problems based on the Mie–Grüneisen EOS show an improved interface resolution. The large-scale interface structures are in good agreement with reference results, and finer small-scale interface structures are recovered in a consistent manner as the grid resolution increases. As compared with reference high grid-resolution numerical results based on AMR algorithms, the interface roll-up phenomena due to the Richtmyer–Meshkov instability and the Kelvin–Helmholtz instability are recovered reliably for shock-bubble interactions involving different ideal gases.