Parallel ILU preconditioning and parallel mesh adaptation with load balancing for general domain decompositions for the Navier-Stokes equations

摘要

A complete framework for solving the incompressible Navier-Stokes equations in parallel is presented. An unstructured mesh is decomposed into non-overlapping subdomains corresponding to the number of processors. Each subdomain is adaptively refined independently based on local Reynolds number estimates. Computational load is balanced by transferring element-octrees between subdomains. A parallel conjugate gradient solver with ILU preconditioning is achieved by resolving node dependencies based on mesh structure. Each node is sorted by category giving an a priori pivoting suited for parallel solution. The parallel solver has convergence rates comparable to serial solvers with a similar ILU strategy.