Robust Multigrid Algorithms For The Incompressible Navier Stokes Equations
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Author | : Ruben S. Montero |
Publisher | : |
Total Pages | : 26 |
Release | : 2000 |
Genre | : Anisotropy |
ISBN | : |
Download Robust Multigrid Algorithms for the Incompressible Navier-Stokes Equations Book in PDF, Epub and Kindle
Anisotropies occur naturally in CFD where the simulation of small scale physical phenomena, such as boundary layers at high Reynolds numbers, causes the grid to be highly stretched leading to a slow down in convergence of multigrid methods. Several approaches aimed at making multigrid a robust solver have been proposed and analyzed in literature using the scalar diffusion equation. However, they have been rarely applied to solving more complicated models, like the incompressible Navier-Stokes equations. This paper contains the first published numerical results of the behavior of two popular robust multigrid approaches (alternating-plane smoothers combined with standard coarsening and plane implicit smoothers combined with semi-coarsening) for solving the 3-D incompressible Navier-Stokes equations in the simulation of the driven cavity and a boundary layer over a flat plate on a stretched grid. The discrete operator is obtained using a staggered-grid arrangement of variables with a finite volume technique and second-order accuracy is achieved using defect correction within the multigrid cycle. Grid size, grid stretching and Reynolds number are the factors considered in evaluating the robustness of the multigrid methods. Both approaches yield large increases in convergence rates over cell-implicit smoothers on stretched grids. The combination of plane implicit smoothers and semi-coarsening was found to be fully robust in the fiat plate simulation up to Reynolds numbers 10(exp 6) and the best alternative in the driven cavity simulation for Reynolds numbers above 10(exp 3). The alternating-plane approach exhibits a better behavior for lower Reynolds numbers (below to 10(exp 3) in the driven cavity simulation. A parallel variant of the smoother, tri-plane ordering, presents a good trade-off between convergence and parallel properties.
Author | : Cornelis W. Oosterlee |
Publisher | : |
Total Pages | : 168 |
Release | : 1993 |
Genre | : Finite element method |
ISBN | : |
Download Robust Multigrid Methods for the Steady and Unsteady Incompressible Navier-Stokes Equations in General Coordinates Book in PDF, Epub and Kindle
Author | : Sergey I. Martynenko |
Publisher | : |
Total Pages | : 198 |
Release | : 2017 |
Genre | : Boundary value problems |
ISBN | : 9783110539271 |
Download The Robust Multigrid Technique Book in PDF, Epub and Kindle
Author | : Cornelis Willebrordus Oosterlee |
Publisher | : |
Total Pages | : 42 |
Release | : 1992 |
Genre | : |
ISBN | : |
Download A Robust Multigrid Method for a Discretization of the Incompressible Navier-Stokes Equations in General Coordinates Book in PDF, Epub and Kindle
Author | : Sergey I. Martynenko |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 264 |
Release | : 2017-09-25 |
Genre | : Mathematics |
ISBN | : 3110537621 |
Download The Robust Multigrid Technique Book in PDF, Epub and Kindle
This book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT) is based on the application of the essential multigrid principle in a single grid algorithm. It results in an extremely simple, very robust and highly parallel solver with close-to-optimal algorithmic complexity and the least number of problem-dependent components. Topics covered include an introduction to the mathematical principles of multigrid methods, a detailed description of RMT, results of convergence analysis and complexity, possible expansion on unstructured grids, numerical experiments and a brief description of multigrid software, parallel RMT and estimations of speed-up and efficiency of the parallel multigrid algorithms, and finally applications of RMT for the numerical solution of the incompressible Navier Stokes equations. Potential readers are graduate students and researchers working in applied and numerical mathematics as well as multigrid practitioners and software programmers. Contents Introduction to multigrid Robust multigrid technique Parallel multigrid methods Applications of multigrid methods in computational fluid dynamics
Author | : Cornelis Willebrordus Oosterlee (Mathematicien.) |
Publisher | : |
Total Pages | : 153 |
Release | : 1993 |
Genre | : |
ISBN | : |
Download Robust Multigrid Methods for the Steady and Unsteady Incompressible Navier-Stokes Equations in General Coordinates Book in PDF, Epub and Kindle
Author | : Michael D. Cain |
Publisher | : |
Total Pages | : 122 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download A Robust Locally Preconditioned Semi-coarsening Multigrid Algorithm for the 2-D Navier-Stokes Equations Book in PDF, Epub and Kindle
Author | : C. W. Oosterlee |
Publisher | : |
Total Pages | : 42 |
Release | : 1992 |
Genre | : |
ISBN | : |
Download A Robust Multigrid Method for a Discretization of the Incompressible Navier-Stokes Equations in General Coordinates Book in PDF, Epub and Kindle
Author | : C. P. Thompson |
Publisher | : |
Total Pages | : 100 |
Release | : 1991 |
Genre | : |
ISBN | : 9788241500800 |
Download Developments in the Solution of the Incompressible Navier Stokes Equations Book in PDF, Epub and Kindle
Author | : Anton Schüller |
Publisher | : |
Total Pages | : 13 |
Release | : 1989 |
Genre | : |
ISBN | : |
Download A multigrid algorithm for the incompressible Navier-Stokes equations Book in PDF, Epub and Kindle