柱坐标下Euler方程数值边界条件的一种处理方法

给出了柱坐标下Euler方程数值边界条件的一种处理方法.径向第一个网格点设在距离中心半点位置上.根据相应物理量的特性,在中心附近进行边界延拓,使得内点的高精度差分格式可以同样应用在网格中心附近,从而无需单侧差分格式,保持了一致的高阶精度.对于周向边界,也建立了一种周期延拓方法,使得在周向所有节点处都能够采用同样的高精度格式离散,并进行了数值试验.

Numerical Boundary Condition of Euler Equations in Cylindrical Coordinate

A method for the treatment of polar singularities of Euler equations is given. The first radial mesh point locates at a half-space away from the centerline. Based on the characteristics of the physical variables, the boundary near centerline is extended so that a high order finite difference scheme can be utilized as at inner mesh points. Similarly, in azimuthal direction the boundary is extended according to the periodicity. An uniform high-order precision is preserved during discretization of equations.