A Compatible Cell-Centered ALE Method Based on General Riemann Solver
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摘要: 深入分析了精确Riemann解法器、MFCAV(Multi Fluid Channel on Averaged Volume)和Dukowicz近似Riemann解法器不能直接应用于相容拉氏方法的原因，通过引入更一般形式的角点算子, 成功将以上3种Riemann解法器应用于新相容拉氏方法中；进一步结合高效的网格重分、重映技术，建立了一种基于任意Riemann解法器的相容中心型显式两步任意拉格朗日-欧拉(ALE)方法。将新的ALE方法应用于数值算例中，结果表明，新ALE方法不仅具有新相容拉氏方法的优点，而且具有处理大变形流动问题的能力。
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关键词:
- 中心型拉氏方法 /
- 交错型拉氏方法 /
- 近似Riemann解法器
Abstract: We first deeply analyzed the reason why the exact Riemann sovler, MFCAV (Multi fluid channel on averaged volume) Riemann solver and Dukowicz Riemann solver cannot be applied directly to the compatible Lagrangian method and then, by introducing a new general nodal solver, we successfully applied the 3 Riemann solvers to the Lagrangian method.Combing the new Lagrangian method with efficiency remesh and remapping technology, we developed a new cell-centered compatible ALE (Arbitrary Lagrangian and Eulerian) method based on arbitrary Riemann solvers.Several numerical examples show that the new ALE method not only has the advantages of the new compatible Lagrangian method, but also has the ability to deal with the large deformation problems. -
图 8 Dukowicz问题在1.3时刻的密度分布计算结果
Figure 8. Density distribution of Dukowicz problem at t=1.3
图 9 Taylor Green Vortex算例在0.75时刻的速度等值线
Figure 9. Velocity contours of Taylor Green Vortex problem at t=0.75
图 10 Taylor Green Vortex算例在x和y方向的熵
Figure 10. Entropy of Taylor Green Vortex problem in x and y direction
图 11 二维Riemann问题在0.52时刻的计算结果
Figure 11. Contours of two-dimensional Riemann problem at t=0.52
图 12 双Mach反射问题在0.60时刻的计算结果
Figure 12. Contours of double Mach reflection problem at t=0.60
表 1 Taylor Green Vortex算例在0.75时刻的误差分析
Table 1. Error analysis of the 3 Riemann solvers for Taylor Green Vortex problem at t=0.75
Grid
numberExact MFCAV Dukowicz L1 error
Convergence
rateL1 error
Convergence
rateL1 error Convergence
rate40 0.357 465 380 0.214 033 305 0.357 462 330 80 0.211 823 462 0.754 7 0.116 933 955 0.872 1 0.211 822 688 0.754 9 160 0.115 855 157 0.870 6 0.061 305 690 0.931 6 0.115 854 999 0.870 5 320 0.060 805 808 0.929 5 0.031 570 952 0.957 4 0.060 805 780 0.930 0 
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