A Stabilizing Algorithm for the Solution of Large Sparse Unsymmetric Matrices with Many Zeros in the Diagonal : A Frontal Solution Program for Steady-State Pressure-Linked Incompressible Hydraulic Problems

Abstract

This paper deals with a study on a stabilizing algorithm for matrices. This algorithm is based on the diagonal pivoting technique in which the order of elimination of equations is controlled, that is, the mass continuity equation is eliminated after the elimination of the momentum equations. The algorithm has been incorporated into a frontal solution program. A comparison of the computer time required for a band matrix algorithm and an earlier frontal method in which the pivot was chosen with that required for the new algorithm was carried out. Advantages of the vectorization of the programming were demonstrated by calculations using scalar and vector processors. To test the stability of the solution obtained by the present algorithm, a cavity driven flow problem under high Re number conditions was analyzed.