TY - JOUR
T1 - Geometric Multigrid Methods on Structured Triangular Grids for Incompressible Navier-Stokes Equations at Low Reynolds Numbers
AU - Gaspar , F. J.
AU - Rodrigo , C.
AU - Heidenreich , E.
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 400
EP - 411
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/534.html
KW - Multigrid methods, Navier-Stokes equations, Vanka smoother, Cavity problem.
AB - <p style="text-align: justify;">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.</p>