用稳定双共轭梯度方法数值求解球坐标系下的Poisson方程

数值求解球坐标系下的Poisson方程，是计算流体力学的一个关键问题.为此提出用稳定双共轭梯度方法，求解了右端源项为-1、 边界值为0 的典型Poisson方程，给出了类似于圆射流计算区域Ω:{r∈[7,52], θ∈[-θb,θb], φ∈[0,2π]， θb=arctan(1/14)}内的数值解，并对数值解及其离散方程的残差进行了讨论.
Abstract：Solving the Poisson equations in spherical coordinate system is a key problem in computational fluid dynamics. Hence, using a conjugate gradient method named Bi-CGSTAB, the typical Poisson equation whose right-hand-side source term is-1 with zero boundary value was solved to give a numerical solution in a domain similar to that in round jet calculation Ω:{ r∈[7,52],  θ∈[-θb,θb], φ∈ [0,2π], θb=arctan(1/14)}. The numerical solution and its relevant residual of discretized equation were discussed.