A vector‐parallel scheme for Navier‐Stokes computations at multi‐gigaflop performance rates

Abstract

AbstractA class of vector‐parallel schemes for solution of steady compressible or incompressible viscous flow is developed and performance studies carried out. The algorithms employ an artificial transient treatment that permits rapid integration to a steady state. In the present work a four‐stage explicit Runge‐Kutta scheme employing variable local step size is utilized for the ODE system integration. The RK‐4 scheme is restructured to allow vectorization and enhance concurrency in the calculation for a streamfunction‐vorticity formulation of the flow problem. The parameters of the resulting RK scheme can be selected to accelerate convergence of the RK recursion. Four main procedures are considered which permit vector‐parallel solution: a Jacobi update, a hybrid of the Jacobi and Gauss‐Seidel method, red‐black ordering and domain decomposition. Numerical performance studies are conducted with a representative viscous incompressible flow calculation. Results indicate that a scheme involving domain decomposition with a Gauss‐Seidel type of update for the RK four‐stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C‐90.