A Comparison Of Different Time Discretization Methods For Unsteady Flows Based On SIMPLE Method

Based on an in-house high-resolution code for steady flows, the discretization forms of the unsteady Navier-Stokes equations, using1st-order implicit and2nd-order implicit temporal schemes are derived and a new code which is based on the SIMPLE method for calculating unsteady flows is established in this paper. The performances of the temporal schemes are compared by calculating the flow over a cylinder and a driven cavity flow. Computational results are compared in order to analyse the accuracy, the convergence and the robustness of different algorithms.It is observed that, higher temporal solution can be obtained by using smaller time step. Since the implicit discretization scheme meets Courant Number unconditionally, a smaller time step will cause a longer computational time and a lower computational efficiency. Studies have also shown that, with the same temporal scheme, the convergence in each step can be faster if the time step is smaller, while the1st-order scheme is slightly faster than the2nd-oder scheme in the same condition. Both schemes have shown good performance of convergence. The accuracy order of velocity for the two schemes are about1, while the accuracy order of pressure is only0.5for the1st-order temporal scheme, and is about1for the2nd-order scheme.Based on this study, the performances of the two temporal schemes are analysed in detail and compared systematically. The results can be of reference for the calculations of unsteady flows using the SIMPLE method.