Simulation of Two-Dimensional Multi-Material Compressible Flows Using Lagrangian Methods
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摘要: 在用拉格朗日方法模拟二维多介质可压缩流体的运动时，网格发生大变形往往是模拟不能正常进行下去的重要原因。网格动态局域重分可以有效改善网格的畸变程度，使计算得以持续。针对三角形计算网格提出了一种新的动态局域重分方法，包含"对角线交换""长边劈裂""短边融合"和"帽子戏法"4种基本操作，其中前3种操作不仅作用于同种介质内部，还可将其拓展到多介质界面处，与"帽子戏法"一起处理界面附近的大变形网格。在网格动态局域重分后，将旧网格上的物理量映射到新网格上，先计算出新三角形的质量和内能，再根据动量守恒和能量守恒对新三角形的格点速度及内能进行修正。利用该方法对冲击波与气泡相互作用和R-T不稳定性问题进行了数值模拟，取得了良好的效果。在R-T不稳定性算例中，采用同种介质和不同介质两种模型进行对比，模拟结果验证了该方法的有效性。Abstract: When simulating the two-dimensional multi-material compressible flows using the Lagrangian method, the distortion of the mesh is often the reason why the process terminates.The dynamic local remeshing is an option to relax the distortion.In this study, we combined the "diagonal-swapping" "edge-splitting" "edge-merging" and "hat-trick" to deal with the distortive mesh.The 4 operations could act not only in single material, but also be extended to the multi-material interface to deal with the distortive mesh on the interface.After the remeshing, the quantities on the old mesh are projected onto the new one.During this process, the mass, momentum and energy are kept conservative.We verified the effectiveness and accuracy of this method by using it to simulate the shock/bubble interaction and the R-T instability.In the R-T instability simulation, the single material and the multi-material models are applied to prove that this method is able to deal with the distortive mesh both inside the material and on the interface.
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图 15 不同时刻24×72网格对应的密度云图(单介质)
Figure 15. Density maps at different time on 24×72 grid (Single material)
图 16 不同时刻48×144网格对应的密度云图(单介质)
Figure 16. Density maps at different time on 48×144 grid (Single material)
图 17 不同时刻100×300网格对应的密度云图(单介质)
Figure 17. Density maps at different time on 100×300 grid (Single material)
图 21 单介质模拟质量、动量及能量的改变量
Figure 21. Variation of mass, momentum and energy in single material simulation
图 22 不同时刻100×300网格的密度云图(多介质)
Figure 22. Material maps at different time on 100×300 grid (Multi-material)
图 23 相同网格下多介质(左)与单介质(右)R-T不稳定性对比
Figure 23. Comparison between multi-material (Left) and single material (Right) R-T instability on the same mesh
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