Geometric multigrid methods on structured triangular grids for incompressible Navier-Stokes equations at low Reynolds numbers

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The main purpose of this work is the efficient implementation of a multigrid algorithmfor 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 finiteelements for the velocities and linear finite elements to approximate the pressure, is used to solvethe problem of flow in a triangular cavity, driven by the uniform motion of one of its side walls. Anappropriate multigrid method for this discretization of Navier-Stokes equations is designed, basedon a Vanka type smoother. Moreover, the data structure used allows an efficient stencil-basedimplementation of the method, which permits us to perform simulations with a large number ofunknowns with low memory consumption and a relatively low computational cost.

Palabras clave
Multigrid methods
Navier-Stokes equations
Vanka smoother
Cavity problem

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