Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781720512141
Category :
Languages : en
Pages : 48
Book Description
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.Swanson, R. C.Langley Research CenterMULTIGRID METHODS; NAVIER-STOKES EQUATION; INCOMPRESSIBLE FLOW; AIRFOILS; TREFFTZ METHOD; RUNGE-KUTTA METHOD; REYNOLDS NUMBER; PARABOLAS; FLAT PLATES; CONVERGENCE; ALGORITHMS
Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781720512141
Category :
Languages : en
Pages : 48
Book Description
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.Swanson, R. C.Langley Research CenterMULTIGRID METHODS; NAVIER-STOKES EQUATION; INCOMPRESSIBLE FLOW; AIRFOILS; TREFFTZ METHOD; RUNGE-KUTTA METHOD; REYNOLDS NUMBER; PARABOLAS; FLAT PLATES; CONVERGENCE; ALGORITHMS
Publisher: Createspace Independent Publishing Platform
ISBN: 9781720512141
Category :
Languages : en
Pages : 48
Book Description
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.Swanson, R. C.Langley Research CenterMULTIGRID METHODS; NAVIER-STOKES EQUATION; INCOMPRESSIBLE FLOW; AIRFOILS; TREFFTZ METHOD; RUNGE-KUTTA METHOD; REYNOLDS NUMBER; PARABOLAS; FLAT PLATES; CONVERGENCE; ALGORITHMS
Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations
Author: R. C. Swanson
Publisher: BiblioGov
ISBN: 9781289262938
Category :
Languages : en
Pages : 50
Book Description
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.
Publisher: BiblioGov
ISBN: 9781289262938
Category :
Languages : en
Pages : 50
Book Description
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.
Multigrid Schemes for Time-dependent Incompressible Navier-Stokes Equations
multigrid methods
Author: Stephen F. Mccormick
Publisher: CRC Press
ISBN: 100010379X
Category : Mathematics
Languages : en
Pages : 665
Book Description
This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.
Publisher: CRC Press
ISBN: 100010379X
Category : Mathematics
Languages : en
Pages : 665
Book Description
This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.
Robust Multigrid Algorithms for the Incompressible Navier-Stokes Equations
Author: Ruben S. Montero
Publisher:
ISBN:
Category : Anisotropy
Languages : en
Pages : 26
Book Description
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.
Publisher:
ISBN:
Category : Anisotropy
Languages : en
Pages : 26
Book Description
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.
Evaluation of Multigrid Acceleration for a Coupled, Strongly Implicit Procedure for the Navier-Stokes Equations
Multigrid Methods VI
Author: Erik Dick
Publisher: Springer Science & Business Media
ISBN: 3642583121
Category : Mathematics
Languages : en
Pages : 306
Book Description
This volume contains 39 of the papers presented at the Sixth European Multigrid Conference, held in Gent, Belgium, September 27-30, 1999. The topics treated at the conference cover all aspects of Multigrid Methods: theory, analysis, computer implementation, applications in the fields of physics, chemistry, fluid mechanics, structural mechanics and magnetism.
Publisher: Springer Science & Business Media
ISBN: 3642583121
Category : Mathematics
Languages : en
Pages : 306
Book Description
This volume contains 39 of the papers presented at the Sixth European Multigrid Conference, held in Gent, Belgium, September 27-30, 1999. The topics treated at the conference cover all aspects of Multigrid Methods: theory, analysis, computer implementation, applications in the fields of physics, chemistry, fluid mechanics, structural mechanics and magnetism.
Algebraic Multigrid Methods for the Numerical Solution of the Incompressible Navier-Stokes Equations
Author: Markus Wabro
Publisher:
ISBN: 9783854875567
Category : Multigrid methods (Numerical analysis)
Languages : en
Pages : 91
Book Description
Publisher:
ISBN: 9783854875567
Category : Multigrid methods (Numerical analysis)
Languages : en
Pages : 91
Book Description
Multigrid Methods
Author: Ulrich Trottenberg
Publisher: Academic Press
ISBN: 9780127010700
Category : Mathematics
Languages : en
Pages : 652
Book Description
Mathematics of Computing -- Numerical Analysis.
Publisher: Academic Press
ISBN: 9780127010700
Category : Mathematics
Languages : en
Pages : 652
Book Description
Mathematics of Computing -- Numerical Analysis.