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Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Multigrid methods are good candidates for the resolution of the system arising in Numerical Fluid Dynamics. However, the question is to know if those algorithms which are efficient for the Poisson equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a Full Multigrid-strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behaviour of the FMG process ... Unstructured, Multigrid, Non-linear, Euler/Navier-Stokes, Steady equations, FMG, O(N) Complexity.
Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Multigrid methods are good candidates for the resolution of the system arising in Numerical Fluid Dynamics. However, the question is to know if those algorithms which are efficient for the Poisson equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a Full Multigrid-strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behaviour of the FMG process ... Unstructured, Multigrid, Non-linear, Euler/Navier-Stokes, Steady equations, FMG, O(N) Complexity.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 392
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Book Description
Author: Laith Abdul Jabbar Zori
Publisher:
ISBN:
Category :
Languages : en
Pages : 340
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Book Description
Author: Michael J. Aftosmis
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 52
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Book Description
A new node based upwind scheme for the solution of the 3D Navier- Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three- dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.
Author:
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ISBN:
Category : Aeronautics
Languages : en
Pages : 702
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Book Description
Author: D. J. Mavriplis
Publisher:
ISBN:
Category :
Languages : en
Pages : 66
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Book Description
Author: David Rafael McDaniel
Publisher:
ISBN:
Category : Aerodynamics
Languages : en
Pages : 600
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Book Description
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722392314
Category :
Languages : en
Pages : 38
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Book Description
A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms. Mavriplis, Dimitri J. and Jameson, Antony and Martinelli, Luigi Langley Research Center NAS1-18107; NAS1-18605; RTOP 505-90-21-01...
Author: Jiri Blazek
Publisher: Elsevier
ISBN: 0080545548
Category : Technology & Engineering
Languages : en
Pages : 461
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Book Description
Computational Fluid Dynamics: Principles and Applications
Author: Dimitri J. Mavriplis
Publisher:
ISBN:
Category : Lift (Aerodynamics)
Languages : en
Pages : 26
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Book Description
A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.
