Computing the velocity of a rotating flow
To compute the time-dependent flow of a rotating incompressible fluid we consider the velocityvorticity formulation of the NavierStokes equations in cylindrical coordinates. In the numerical method employed the velocity field at each time-step is found as the least squares solution of an overdetermined system of linear equations, Ax=b. We consider how to compute x using the preconditioned conjugate gradient algorithm for least squares (PCGLS) on a distributed parallel computer. The various aspects of using a parallel computer are discussed, and results for a wide range of parallel computers are presented. The parallel speed-up depends on the architecture but is typically about 80% of the number of processors used.
least squares conjugate gradients parallel computers cauchyriemann equations overdetermined linear system of equations