An SOR implicit time-accurate scheme in calculating unsteady flows

A new time-accurate marching scheme for unsteady flow calculations is proposed in the present work. This method is the combination of classical Successive Over-Relaxation (SOR) iteration method and Jacobian matrix diagonally dominant splitting method of LUSGS. One advantage of this algorithm is the second-order accuracy because of no factorization error. Another advantage is the low computational cost because the Jacobian matrices and fluxes are only calculated once in each physical time step. And, the SOR algorithm has better convergence property than Gauss-Seidel. To investigate its accuracy and convergency, several unsteady flow computational tests are carried out by using the proposed SOR algorithm. Roe's FDS scheme is used to discritize the inviscid flux terms. Unsteady computational results of SOR are compared with the experiment results and those of Gauss-Seidel. Results reveal that the numerical results agree well with the experimental data and the second-order accuracy can be obtained as the Gauss-Seidel for unsteady flow computations. The impact of SOR factor is investigated for unsteady computations by using different SOR factors in this algorithm to simulate each computational test. Different numbers of inner iterations are needed to converge to the same criterion for different SOR factors and optimal choice of SOR factor can improve the computational efficiency greatly.