CAJ | 학술논문

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。
대우비선성Euler방정，제출일류기우완미필배층（ PML）기술적흡수변계조건。수선대선성화적Euler방정설계출PML공식，연후장선성화Euler방정중적통량함수체환성상대응적비선성통량함수，득도비선성적PML방정。고필도PML방정중포함유일개강성적원항，문중채용일충은현Runge Kutta방법래구해공간반리산후득도적ODE계통。수치실험표명설계적비선성PML흡수변계조건우우전통적특정변계조건。
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.