Computing interface motion in compressible gas dynamics
Computing interface motion in compressible gas dynamics
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DOI：
10.1016/0021-9991(92)90229-r
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发表时间：
1992-06
影响因子：
4.1
通讯作者：
W. Mulder;S. Osher;J. Sethian
中科院分区：
文献类型：
--
作者：
W. Mulder;S. Osher;J. Sethian
Osher和Sethian最近提出了传播界面运动方程的“Hamilton-Jacobi”水平集公式。这个公式允许前线自相交，发展奇点，并改变拓扑结构。基于这种方法的数值算法自然地处理拓扑合并和断裂，在任何数量的空间维度中工作，并且不需要将移动前沿写为函数。取而代之的是，移动前嵌入作为一个特定的水平集在一个固定的域偏微分方程。借用双曲守恒律的数值技术，然后用来准确地捕捉复杂的表面运动，满足全局熵条件的传播前Sethian。在本文中，我们分析了这个水平集制剂的可压缩气体动力学的守恒律系统的耦合。我们研究了水平集函数的保守差分和非保守差分，并对这两种方法进行了比较。为了说明该方法的能力，我们研究了空气-空气和空气-氦气边界的可压缩Rayleigh-Taylor和Kelvin-Helmholtz不稳定性。我们进行数值收敛性研究的方法在一定范围内的参数，并分析这种方法适用于这些问题的准确性。
A “Hamilton-Jacobi” level set formulation of the equations of motion for propagating interfaces has been introduced recently by Osher and Sethian. This formulation allows fronts to self-intersect, develop singularities, and change topology. The numerical algorithms based on this approach handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving front be written as a function. Instead, the moving front is embedded as a particular level set in a fixed domain partial differential equation. Numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by Sethian. In this paper, we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics. We study both conservative and non-conservative differencing of the level set function and compare the two approaches. To illustrate the capability of the method, we study the compressible Rayleigh-Taylor and Kelvin-Helmholtz instabilities for air-air and air-helium boundaries. We perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems.