二维蛙跳格式的离散透明边界条件
Discrete transparent boundary conditions for the two-dimensional leap-frog scheme
摘要：
我们开发了一个通用的策略，以实现（近似）离散透明边界条件的有限差分近似的二维输运方程。计算域是一个配备笛卡尔网格的矩形。对于二维蛙跳方案，我们解释了为什么我们的策略提供了明确的数值边界条件的四个边的矩形，为什么它不需要规定任何条件的四个角的计算域。通过简正模态分析，分析了矩形各边数值边界条件的稳定性。对矩形上全问题的数值研究表明，当在矩形的每一边耦合稳定策略时，可能会出现强不稳定性。其他耦合策略产生有希望的结果。
英文摘要：
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with a Cartesian grid. For the two-dimensional leapfrog scheme, we explain why our strategy provides with explicit numerical boundary conditions on the four sides of the rectangle and why it does not require prescribing any condition at the four corners of the computational domain. The stability of the numerical boundary condition on each side of the rectangle is analyzed by means of the so-called normal mode analysis. Numerical investigations for the full problem on the rectangle show that strong instabilities may occur when coupling stable strategies on each side of the rectangle. Other coupling strategies yield promising results.
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