WIT Press

A Parallel ILU Strategy For Solving Navier-Stokes Equations On An Unstructured 3D Mesh


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WIT Press


Ø. Staff & S. Ø. Wille


An iterative algorithm for solving a mixed finite element formulation of Navier- Stokes equations on a distributed memory computer is presented. The solver is a Krylov subspace method with a parallel preconditioner suitable for high latency clusters. Nodes are pivoted to minimize the number of synchronization points in each solver iteration. An unstructured mesh is decomposed into non-overlapping subdomains. Each node is given a category depending on which subdomains it is a member of and on the subdomains of its neighboring nodes in the mesh. Based on these categories, an a priori pivoting suited for parallel solution is constructed. The solver requires approximately the same number of iterations as good serial solvers with a similar preconditioner. The incomplete LU (ILU) preconditioning and subsequent solve is performed on a global matrix implicitly formed as a sum of all subdomain matrices. Communication overhead is kept low by generating a schedule to send information to neighboring subdomains as soon as dependencies in the matrix are resolved. Results will be shown to indicate that this is a viable strategy on computer clusters built with cheap off the shelf components. Keywords: ILU, preconditioning, parallel, unstructuredmesh, CFD, Navier-Stokes. 1 Introduction Simulations on single processors are often limited by CPU speed and available central memory. Even fairly modest three dimensional problems can surpass what


ILU, preconditioning, parallel, unstructuredmesh, CFD, Navier-Stokes.