非线性欧拉方程组的完美匹配层吸收边界条件

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。

PML Absorbing Boundary Conditions for Nonlinear Euler Equations

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.