Int. J. Numer. Anal. Mod., 11 (2014), pp. 400-411. |
Geometric multigrid methods on structured triangular grids for incompressible Navier-Stokes equations at low Reynolds numbers F. J. Gaspar ^{1}, C. Rodrigo ^{1}, E. Heidenreich ^{2} 1 IUMA, Department of Applied Mathematics, University of Zaragoza, Spain2 Departamento de Ingeniería Mecánica, Escuela Superior Técnica; Instituto de Investigaciones Científicas y Técnicas para la Defensa, Villa Martelli, Buenos Aires, Argentina Received by the editors October 30, 2012 and, in revised form, July 6, 2013 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. AMS subject classifications: 65N55, 65F10Key words: Multigrid methods, Navier-Stokes equations, Vanka smoother, Cavity problem. Email: fjgaspar@unizar.es, carmenr@unizar.es, elvioh@citefa.gov.ar |