APPLICATION OF THE FULL APPROXIMATION STORAGE METHOD TO THE NUMERICAL-SIMULATION OF 2-DIMENSIONAL STEADY INCOMPRESSIBLE VISCOUS MULTIPHASE FLOWS

In recent years multigrid algorithms have been applied to increasingly difficult systems of partial differential equations and major improve ments in both speed of convergence and robustness have been achieved. Problems involving several interacting fluids are of great interest in many industrial applications, especially in the process and petro-che mical sectors. However, the multifluid version of the Navier-Stokes eq uations is extremely complex and represents a challenge to advanced nu merical algorithms. In this paper, we describe an extension of the ful l approximation storage (FAS) multigrid algorithm to the multifluid eq uations. A number of special issues had to be addressed. The first was the development of a customised, non-linear, coupled relaxation schem e for the smoothing step. Automatic differentiation was used to facili tate the coding of a robust, globally convergent quasi-Newton method. It was also necessary to use special inter-grid transfer operators to maintain the realisability of the solution. Algorithmic details are gi ven and solutions for a series of test problems are compared with thos e from a widely validated, commercial code. The new approach has prove d to be robust; it achieves convergence without resorting to specialis ed initialisation methods. Moreover, even though the rate of convergen ce is complex, the method has achieved very good reduction factors: ty pically five orders of magnitude in 50 cycles. (C) 1998 John Wiley & S ons, Ltd.