Investigation Of Implicit Time Integration Methods With High-order Accurate Scheme

Focusing on high-order weighted compact nonlinear scheme(WCNS),the performance of two types of implicit time integration methods are studied.One is data-parallel lower-upper relaxation method(DP-LUR),which is adapt from lower-upper symmetric Gauss-Seidel method(LU-SGS).Compared with LU-SGS method,DP-LUR method is shown to have good convergence properties on many problems and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid.The other is data-parallel line relaxation method(DPLR),which is adapt from Gauss-Seidel line relaxation method(GSLR).The convergence properties of DPLR method is sensitive to the way to calculate the inviscous Jacobian matrix.Direct implicit simulation of complex steady state flows is usually too difficult numerically in the absence of a good initial guess.A delicate choice of the time steps,or the CFL numbers is crucial to reduce the number of iterations.The existing strategies 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).We propose an strategy for the automatic determination of the CFL numbers,which use several metrics to estimate the convergence rate and the possibility of breakdowns.It then takes appropriate actions.We use this strategy on LU-SGS,DP-LUR and DPLR method.Numerical results obtained on several test cases show a systematic reduction of the total number of iterations.,and breakdowns are avoided while convergence is almost guaranteed.