A comparison of different numerical schemes in spherical Couette flow simulation

We compare the performance of line Gauss–Seidel (LGS), point Gauss–Seidel (PGS), and alternating direction implicit (ADI) linear solvers used in the artificial compressibility method for the numerical solution of the three-dimensional incompressible Navier–Stokes equations. Spatial discretization is carried out using a fifth-order WENO scheme for the convective terms and a second-order central difference scheme for the viscous terms. A comparison is made by simulating the spherical Couette flow problem, with only the inner sphere rotating and the outer one fixed. OpenMP is used for numerical computation in parallel for the three schemes. First, we compare the numerical efficiency of the solvers by computing 0-vortex flow for a medium-gap σ=R2−R1/R1=0.25. Second, we make a residual comparison for a steady-state flow calculation based on the CFL number and artificial compressibility factor. Finally, we compare the three solvers for unsteady flow computations based on the artificial compressibility factor. The results show that the LGS solver is more reliable than the PGS and the ADI solvers. To show the accuracy of the LGS scheme, we compute different flow modes for an intermediate-gap clearance ratio σ=R2−R1/R1=0.14. The computed results have good agreement with the existing numerical results.