Large implicit finite element simulations of time-dependent incompressible flows on scalable parallel systems

Abstract

An efficient numerical scheme to solve the time-dependent incompressible Navier-Stokes equations was implemented for vector-super-computers [2] and distributed parallel systems [4]. The approximate ’projection 2’ method [7] allows the decoupled solution of the components of the momentum equation and the continuity equation. Element level divergence free finite elements and irregular meshes approximate arbitrary geometries. Time-dependent boundary conditions on curved surfaces are possible. The parallel version of the code uses a parallel data structure as in domain decomposition. The implicit systems of equations are assembled for submeshes on distributed processors and all data and matrices are always kept local. Iterative conjugate gradient methods solve the implicit systems of equations for the intire computational domain, while they work on the local data and employ block preconditioning on the submeshes. The method always obtains exactly the sequential solution while it does the works on parallel processors. The parallel version allows high spatial resolution because the feasible problem size grows linearly with the amount of distributed memory.