Numerical solution to the Poisson equation under the spherical coordinate system with Bi-CGSTAB method

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.