METHODS FOR REDUCING APPROXIMATE-FACTORIZATION ERRORS IN 2-FACTORED AND 3-FACTORED SCHEMES

Three methods are presented for reducing approximate-factorization (AF) errors that exist in two- and three-factored schemes, such as the popular ADI, LU, and LU-SSOR methods. For problems in which AF errors are larger than both time-discretization and time-linearization errors, these methods can be used to lower the AF errors so that larger time-step sizes can be used when transient solutions are of interest. When only steady-state solutions are of interest, these methods can be used to accelerate the convergence rate. The methods presented also can be used to stabilize schemes that are unstable because of AF errors (e.g., the three-factored ADI scheme applied to the linear advection equation with central-difference approximation of the spatial derivatives). The three methods presented can be added easily to existing codes using any two- or three-factored schemes.