A two and threedimensional fluid flow analysis system using a fast linear system solver
Abstract
Researchers propose a preconditioned conjugate gradient type method suited to supercomputers for solving large sparse nonsymmetric linear systems arising in finite difference fluid flow analysis which employ boundaryfitted coordinates. In twodimensional analysis, by using only the 5point finite difference matrix as the preconditioner, the linear systems can be solved efficiently by the Tridiagonal Factorization conjugate gradient square (CGS) algorithm, which can be easily vectorized. The method is also applicable to threedimensional problems by using the 7point finite difference matrix as the preconditioner. These techniques are employed to realize a fast 3D fluid flow simulation system. Numerical experiments were done on the NEC SX2 supercomputer. Results show that the Tridiagonal Factorization CGS (TFCGS) algorithm is 1.3 times faster than the conventional incomplete lowerupper CGS method. By using the 7point TFCGS method, a very high vector ratio of 99.9 percent is achieved, and the computation speed of the vector mode is 53 times as fast as that of the scalar mode.
 Publication:

7th NAL Symposium on Aircraft Computational Aerodynamics
 Pub Date:
 1989
 Bibcode:
 1989saca.proc...19A
 Keywords:

 Computational Fluid Dynamics;
 Computerized Simulation;
 Conjugate Gradient Method;
 Linear Systems;
 Supercomputers;
 Three Dimensional Flow;
 Algorithms;
 Coordinates;
 Factorization;
 Finite Difference Theory;
 Scalars;
 Fluid Mechanics and Heat Transfer