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Volume 11, Issue 2
Geometric Multigrid Methods on Structured Triangular Grids for Incompressible Navier-Stokes Equations at Low Reynolds Numbers

F. J. Gaspar, C. Rodrigo & E. Heidenreich

Int. J. Numer. Anal. Mod., 11 (2014), pp. 400-411.

Published online: 2014-11

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  • 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.

  • Keywords

Multigrid methods, Navier-Stokes equations, Vanka smoother, Cavity problem.

  • AMS Subject Headings

65N55, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-400, author = {Gaspar , F. J.Rodrigo , C. and Heidenreich , E.}, title = {Geometric Multigrid Methods on Structured Triangular Grids for Incompressible Navier-Stokes Equations at Low Reynolds Numbers}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/534.html} }
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 -

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.

Gaspar , F. J.Rodrigo , C. and Heidenreich , E.. (2014). Geometric Multigrid Methods on Structured Triangular Grids for Incompressible Navier-Stokes Equations at Low Reynolds Numbers. International Journal of Numerical Analysis and Modeling. 11 (2). 400-411. doi:
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