非线性欧拉方程组的完美匹配层吸收边界条件(英文)

PML Absorbing Boundary Conditions for Nonlinear Euler Equations

对于非线性Euler方程,提出一类基于完美匹配层(PML)技术的吸收边界条件。首先对线性化的Euler方程设计出PML公式,然后将线性化Euler方程中的通量函数替换成相对应的非线性通量函数,得到非线性的PML方程。考虑到PML方程中包含有一个刚性的源项,文中采用一种隐显Runge-Kutta方法来求解空间半离散后得到的ODE系统。数值实验表明设计的非线性PML吸收边界条件优于传统的特征边界条件。

Perfectly matched layer ( PML ) absorbing boundary conditions ( ABC ) are presented for nonlinear Euler equations in unbounded domains. The basic idea consists of two steps. First, PML technique is applied to linearized Euler equations in either a uniform mean flow or a parallel mean flow. Nonlinear PML equations are then derived by replacing flux functions in linearized Euler equations with nonlinear counterparts. Since a stiff source term gets involved in PML equations, an implicit-explicit Runge-Kutta scheme is proposed to integrate discrete ODE system. Numerical experiments are performed. They demonstrate advantage of proposed PML ABC over traditional characteristic boundary condition.