一种渐变无反射边界条件的建立与验证

建立并验证了一种适用于非线性流动的新无反射边界条件，以简单的迁移方程模型为基础，提出了一种通量渐变消失无反射边界条件。通过乘以合适的函数，在渐变层内偏微分方程中的空间偏导项逐渐消失，从而在边界点上得到只含有时间变量的常微分方程，来解决自由区域处边界造成的定解问题。将渐变边界条件推广到了一维和二维非线性Euler方程，其方程形式简单，便于实现。在计算域边界处采用空间滤波和二维情形时角区内引入牛顿阻尼区提高了渐变边界条件的数值稳定性。在非线性情况下对二维Euler方程渐变边界条件进行了一系列的数值验证，得到了令人满意的数值结果。

Construction and validation of a gradually diminished flux nonreflecting boundary condition

A new nonreflecting boundary condition applicable for nonlinear flows is constructed and validated. It is proposed by using Gradually Diminished Flux （GDF） based on a simple convection equation. Through multiplying the flux term by a proper function, the GDF equation is constructed with a width of a few grid points at boundary regions, obtaining a well-posed ordinary differential equation for numerical computation at the outermost point. The GDF is extended to one and two dimensional nonlinear Euler equations with a simple appearance easy for implementation. The numerical stability is improved by introducing a spatial filter in the boundary region and a Newtonian cooling/friction zone for two dimensions inside the surrounding comer. The GDF boundary condition for two dimensional Euler equations is validated by several nonlinear numerical examples, with satisfactory results reported.