| Abstract: | Various pressure-based schemes are proposed for transient flows based on well-established SIMPLE and PISO algorithms. The schemes are applied to the solution of unsteady laminar flow around a square cylinder and steady laminar flow over a backward-facing step. The implicit treatment and the performance of the various schemes are evaluated by using benchmark solutions with a small time step. Three different second-order-accurate time derivatives based on different time levels are presented. The different time derivatives are applied to the various schemes under consideration. Overall the PISO scheme was found to predict accurate results and was robust. However, for small time step values, alternative schemes can predict accurate results for approximately half the computational cost. The choice of time derivative proved to be very significant in terms of the accuracy and robustness of a scheme. Significantly, the one-sided forward differencing scheme was the most successful used in conjunction with a strongly implicit-based algorithm. However, a greater degree of accuracy was achieved using the standard PISO algorithm with the Crank–Nicolson time derivative. Recommendations for future work are discussed. © 1998 John Wiley & Sons, Ltd. |
