Purely algebraic domain decomposition methods for the incompressible Navier-Stokes equations
Abstract
In the context of non overlapping domain decomposition methods, several algebraic approximations of the Dirichlet-to-Neumann (DtN) map are proposed in [F. X. Roux, et. al. Algebraic approximation of Dirichlet- to-Neumann maps for the equations of linear elasticity, Comput. Methods Appl. Mech. Engrg., 195, 2006, 3742-3759]. For the case of non overlapping domains, approximation to the DtN are analogous to the approximation of the Schur complements in the incomplete multilevel block factorization. In this work, several original and purely algebraic (based on graph of the matrix) domain decomposition techniques are investigated for steady state incompressible Navier-Stokes equation defined on uniform and stretched grid for low viscosity. Moreover, the methods proposed are highly parallel during both setup and application phase. Spectral and numerical analysis of the methods are also presented.
Keywords
Cite
@article{arxiv.1104.3349,
title = {Purely algebraic domain decomposition methods for the incompressible Navier-Stokes equations},
author = {Pawan Kumar},
journal= {arXiv preprint arXiv:1104.3349},
year = {2011}
}
Comments
Introduction rewritten, Comparison with state-of-art methods added, figure on overlapping case added, Complete algorithms added to build and solve with the preconditioners, Tests with Reynold number 3000 added, some observations with block jacobi method in analysis section