Geometric Multigrid Methods on Structured Triangular Grids for Incompressible Navier-Stokes Equations at Low Reynolds Numbers
Year: 2014
Author: F. J. Gaspar, C. Rodrigo, E. Heidenreich
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 2 : pp. 400–411
Abstract
The main purpose of this work is the efficient implementation of a multigrid algorithm for solving Navier-Stokes problems at low Reynolds numbers in different triangular geometries. In particular, a finite element formulation of the Navier-Stokes equations, using quadratic finite elements for the velocities and linear finite elements to approximate the pressure, is used to solve the problem of flow in a triangular cavity, driven by the uniform motion of one of its side walls. An appropriate multigrid method for this discretization of Navier-Stokes equations is designed, based on a Vanka type smoother. Moreover, the data structure used allows an efficient stencil-based implementation of the method, which permits us to perform simulations with a large number of unknowns with low memory consumption and a relatively low computational cost.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-534
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 2 : pp. 400–411
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Multigrid methods Navier-Stokes equations Vanka smoother Cavity problem.