基于非结构网格二维 Euler 方程的 Jameson 求解方法
摘 要
本文介绍了基于非结构网格求解二维 Euler 方程的 Jameson 中心格式方法。在空间离散
上采用的是有限体积法，时间上采用的是四步显式 Runge－Kutta 迭代求得最后的定常解。
人工耗散项为守恒变量的二阶和四阶差分项。边界条件采用的是无反射边界条件，并采用当
地时间步长进行加速收敛。最后对翼型绕流进行了数值模拟，结果比较令人满意。
关键词：Jameson 中心格式，Euler 方程，非结构网格，有限体积法
Abstract
A method for the numerical solution of the two-dimensional Euler equations on unstructured
grids has been developed. The cell-centred symmetric finite-volume spatial discretisation is applied
in a general formulation. The integration in time, to a steady-state solution, is performed using an
explicit, four-stage Runge－Kutta procedure. The artificial dissipation is constructed as a blending
of second and fourth differences of the conserved variables. And in the boundary, there is none of
the outgoing waves are reflected back into the computational domain. An acceleration technique
called local time stepping is used. At last, standard test cases for both subsonic and supersonic flows
have been used to validate the method.
Keyword: Jameson method, Euler equations, unstructured grid，finite-volume
