论文标题
力矩方法作为数值求解器：冲击结构问题的挑战
Moment method as a numerical solver: Challenge from shock structure problems
论文作者
论文摘要
我们调查了许多时刻层次结构，并在计算一维冲击结构中测试了它们的性能。发现对于高马赫数，层次结构在计算上是昂贵的，要么难于收敛，因此这些方法可疑地仿真了高度非平衡流。通过检查Grad Moment方法的收敛问题，我们提出了一个新的力矩层次结构来桥接流体动力学模型和动力学方程，从而使非线性力矩方法可以用作数值工具，以使高速流的速度空间离散。对于一维速度，该方法是针对奇数矩制定的，并且可以无缝扩展到三维情况。数值测试表明，该方法能够准确地预测具有高马赫数的冲击结构，并且随着矩数的增加，结果会收敛到玻尔兹曼方程的解。还考虑了冲击结构问题以外的某些应用，表明所提出的方法适用于过渡流的计算。
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge, making these methods questionable for the simulation of highly non-equilibrium flows. By examining the convergence issue of Grad's moment methods, we propose a new moment hierarchy to bridge the hydrodynamic models and the kinetic equation, allowing nonlinear moment methods to be used as a numerical tool to discretize the velocity space for high-speed flows. For the case of one-dimensional velocity, the method is formulated for odd number of moments, and it can be extended seamlessly to the three-dimensional case. Numerical tests show that the method is capable of predicting shock structures with high Mach numbers accurately, and the results converge to the solution of the Boltzmann equation as the number of moments increases. Some applications beyond the shock structure problem are also considered, indicating that the proposed method is suitable for the computation of transitional flows.
