Coarse grain parallel finite element simulations for incompressible flows

Coarse Grain Parallel Finite Element Simulations for Incompressible Flows

Parallel simulation of incompressible fluid flows is considered on networks of homogeneous workstations. Coarse-grain parallelization of a Taylor–Galerkin/pressure–correction finite element algorithm are discussed, taking into account network communication costs. The main issues include the parallelization of system assembly, and iterative and direct solvers, that are of common interest to fini...

PARALLEL FINITE ELEMENT COMPUTATION OF 3D INCOMPRESSIBLE FLOWS ON MPPs

In this chapter we present numerical simulations of the Navier-Stokes equations with the stabilized finite element methods on the massively parallel CM-5 supercomputer. These computations are based on implicit methods and their implementations are based on the assumption that the mesh is unstructured. The use of matrix-free iterations eliminates the need to store element-level matrices, thus pr...

Gauge finite element method for incompressible flows

A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that aris...

Simple finite element method in vorticity formulation for incompressible flows

A very simple and eÆcient nite element method is introduced for two and three dimensional viscous incompressible ows using the vorticity formulation. The method relies on recasting traditional nite element method in the spirit of the high order accurate nite di erence methods introduced by the authors in [10]. Optimal accuracy of arbitrary order can be achieved using standard nite element or sp...

hTools for Predicting Incompressible Flows via Nonconforming Finite Element Models