时间对称ADI与因果重联：双曲型方程组的动网格稳定数值方法
Time-Symmetric ADI and Causal Reconnection: Stable Numerical Techniques for Hyperbolic Systems on Moving Grids
摘要：
动网格在流体力学问题的数值求解和数值相对论中有着重要的意义。我们发现，传统的积分方法的简单波动方程在一个和多个维度上表现出一些不稳定性的移动网格。我们介绍两种技术，我们称之为因果重联和时间对称ADI，这两种技术一起允许整合的波动方程的绝对局部稳定性在任何数量的维度上的网格，可能会移动得比波速快得多，甚至可以加速。这些方法允许很长的时间步长，是完全二阶精度，并提供算子分裂的计算效率。
英文摘要：
Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of instabilities on moving grids. We introduce two techniques, which we call causal reconnection and time-symmetric ADI, which together allow integration of the wave equation with absolute local stability in any number of dimensions on grids that may move very much faster than the wave speed and that can even accelerate. These methods allow very long time-steps, are fully second-order accurate, and offer the computational efficiency of operator-splitting.
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