A dynamic adaption algorithm for grid, time and satellite processors for nodal finite element formulations of Navier-Stokes equations

Abstract

Two parallel nodal finite element algorithms for solving the Navier-Stokes equations are developed. The algorithms are based on operator splitting of the original Navier-Stokes equations. Linear basis functions are applied in the finite element formulation of the equation system. The finite element grid is generated by the Tri-Tree grid generation algorithm. The grid is adapted to the solution according to the element Reynolds number. The length of each time step is computed from the Courant number. The linearized equation system is solved iteratively by conjugate gradient algorithms. The most time-consuming part of the conjugate gradient algorithm, the generation of the right-hand side of the equation system and the matrix-vector multiplication, is distributed to satellite processors. The number of processors which can be used by the parallel algorithm is only limited by the number of finite elements or the number of processors available. The parallel algorithm can either select a fixed number of satellite processors or the number of satellite processors can be adapted to the amount of work performed during the computations.