Commun. Comput. Phys.,
A Scalable Domain Decomposition Method for Ultra-Parallel Arterial Flow Simulations
Leopold Grinberg 1, George Em Karniadakis 1*1 Division of Applied Mathematics, Brown University, Providence 02912, USA.
Received 18 March 2008; Accepted (in revised version) 10 July 2008
Available online 9 September 2008
Ultra-parallel flow simulations on hundreds of thousands of processors require new multi-level domain decomposition methods. Here we present such a new two-level method that has features both of discontinuous and continuous Galerkin formulations. Specifically, at the coarse level the domain is subdivided into several big patches and within each patch a spectral element discretization (fine level) is employed. New interface conditions for the Navier-Stokes equations are developed to connect the patches, relaxing the $C^0$ continuity and minimizing data transfer at the patch interface. We perform several 3D flow simulations of a benchmark problem and of arterial flows to evaluate the performance of the new method and investigate its accuracy.AMS subject classifications: 52B10, 65D18, 68U05, 68U07
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Key words: Bioflows, spectral elements, discontinuous Galerkin, parallel computing.
Email: email@example.com (L. Grinberg), firstname.lastname@example.org (G. K. Karniadakis)