Simultaneous Solution Algorithms for Gas-Solid Flows: An Efficient Parallel Line Solver

A pointwise simultaneous solution algorithm based on dual time stepping was developed by De Wilde et al. (2002). With increasing grid aspect ratios, the efficiency of the point method quickly drops. Most realistic flow cases, however, require high grid aspect ratio grids, with the highest grid spacing in the streamwise direction. In this direction, the stiffness is efficiently removed by applying preconditioning (Weiss and Smith, 1995). In the direction perpendicular to the stream wise direction, stiffness remains because of the viscous and the acoustic terms. To resolve this problem, a line method is presented. All nodes in a plane perpendicular to the stream wise direction, a so-called line, are solved simultaneously. This allows a fully implicit treatment of the fluxes in the line, removing the stiffness in the line wise directions. Calculations with different grid aspect ratios are presented to investigate the convergence behavior of the line method. The line method presented is particularly suited for parallelization. At each pseudo-time step, the lines (typically hundreds) can be solved independently of each other. The Message Passing Interface (MPI) standard (Snir et al., 1996) is used. The communication between the processors can be easily reduced by solving a block of lines per processor. The communication is then limited to information regarding only the outer lines of the block. In common practice, the number of lines is much higher than the number of processors available. In this region of the lines/processor space, the reduction of the calculation time is linear with the number of processors that is used.Copyright © 2004 by ASME