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Developing an efficient multigrid strategy for solving incompressible flow

Darbandi, M ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1115/IMECE2004-60710
  3. Publisher: 2004
  4. Abstract:
  5. In this work, a multigrid acceleration technique is suitably developed for solving the two-dimensional incompressible Navier-Stokes equations using an implicit finite element volume method. In this regard, the solution domain is broken into a huge number of quadrilateral finite elements. The accurate numerical solution of a flow field can be achieved if very fine grid resolutions are utilized. Unfortunately, the standard implicit solvers need more computational time to solve larger size of algebraic set of equations which normally arise if fine grid distributions are used. Past experience has shown that the convergence of classical relaxation schemes perform an initial rapid decrease of residuals followed by a slower rate of decrease. This point indicates that a relaxation procedure is efficient for eliminating only the high frequency components of the residuals. This problem can be over-come using multigrid method, i.e., carrying out the relaxation procedure on a series of different grid sizes. There are different prolongation operators to establish a multigrid procedure. A new prolongation expression is suitably developed in this work. It needs constructing data during refining and coarsening stages which is fulfilled using suitable finite element interpolators. The extended formulations are finally used to test several different problems with available benchmark solutions. The results indicate that the current multigrid strategy effectively improves the bandit solver performance. Copyright © 2004 by ASME
  6. Keywords:
  7. Boundary conditions ; Viscosity ; Vectors ; Two dimensional ; Specific heat ; Reynolds number ; Navier Stokes equations ; Iterative methods ; Finite element method ; Convergence of numerical methods ; Computational methods ; Channel flow
  8. Source: 2004 ASME International Mechanical Engineering Congress and Exposition, IMECE 2004, Anaheim, CA, 13 November 2004 through 19 November 2004 ; Volume 260 , 2004 , Pages 625-634 ; 08888116 (ISSN)
  9. URL: https://asmedigitalcollection.asme.org/IMECE/proceedings/IMECE2004/47098/625/300553