An Expert-system to Control the Cfl Number of Implicit Upwind Methods an Expert-system to Control the Cfl Number of Implicit Upwind Methods an Expert-system to Control the Cfl Number of Implicit Upwind Methods

Direct implicit simulation of complex steady state ows is usually too dii-cult numerically in the absence of a good initial guess. \Pseudo-transient-continuation" is a physically motivated technique that follows the physical transient solution starting from a uniform ow. Here, a delicate choice of the time steps, or the CFL numbers is crucial to reduce the number of iterations. However , existing strategies such as exponential laws (EXP) or residual-norm based strategies (SER) are not robust; if some initial parameters are not carefully chosen, they may produce an excessive number of iterations or produce non-physical states (breakdowns). In this paper, we investigate this problem and propose an expert-system for the automatic determination of the CFL numbers. This expert-system uses several metrics to estimate the convergence rate and the possibility of breakdowns. It then takes the appropriate actions. Numerical results obtained on a wide variety of test cases show a systematic reduction of the total number of iterations compared to SER or EXP. Furthermore, the system seems more robust in the sense that iteration counts depend only slightly on the parameters, and breakdowns are avoided while convergence is almost guaranteed. Abstract Direct implicit simulation of complex steady state ows is usually too dif-cult numerically in the absence of a good initial guess. \Pseudo-transient-continuation" is a physically motivated technique that follows the physical transient solution starting from a uniform ow. Here, a delicate choice of the time steps, or the CFL numbers is crucial to reduce the number of iterations. However, existing strategies such as exponential laws (EXP) or residual-norm based strategies (SER) are not robust; if some initial parameters are not carefully chosen, they may produce an excessive number of iterations or produce non-physical states (breakdowns). In this paper, we investigate this problem and propose an expert-system for the automatic determination of the CFL numbers. This expert-system uses several metrics to estimate the convergence rate and the possibility of breakdowns. It then takes the appropriate actions. Numerical results obtained on a wide variety of test cases show a systematic reduction of the total number of iterations compared to SER or EXP. Furthermore, the system seems more robust in the sense that iteration counts depend only slightly on the parameters, and breakdowns are avoided while convergence is almost guaranteed.