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multigrid algorithms for nonconforming and mixed methods for nonsymmetric and indefinite problems

SIAM JOURNAL ON SCIENTIFIC COMPUTING 1998年第2期19卷 502-515页

作者： Chen, ZX Kwak, DY Yon, YJ So Methodist Univ Dept Math Dallas TX 75275 USA Korea Adv Inst Sci & Technol Dept Math Taejon 305701 South Korea

In this paper we consider multigrid algorithms for nonconforming and mixed finite element methods for nonsymmetric and/or indefinite elliptic problems. We show that a simple V-cycle multigrid iteration using conforming coarse-grid corrections converges at a uniform rate provided that the coarsest level in the multilevel iteration is sufficiently fine (but independent of the number of multigrid levels). Various types of smoothers for the nonsymmetric and indefinite problems are discussed. Extensive numerical results are presented.

关键词： mixed method nonconforming method finite elements multigrid algorithm convergence nonsymmetric and/or indefinite problems

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Fast corner detection

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IMAGE AND VISION COMPUTING 1998年第2期16卷 75-87页

作者： Trajkovic, M Hedley, M Univ Sydney Dept Elect Engn Sydney NSW 2006 Australia

This paper describes a new corner detection algorithm, based on the property of corners that the change of image intensity should be high in all directions. Consequently, the corner response function (CRF) is computed as a minimum change of intensity over all possible directions. To compute the intensity change in an arbitrary direction an interpixel approximation is used. A multigrid approach is employed to reduce the computational complexity and to improve the quality of the detected corners. This algorithm, and other popular corner detectors, were evaluated and compared on the basis of their consistency, accuracy and speed using a range of images and video sequences. It was found that our algorithm performs well compared to the other algorithms, but it is significantly faster to compute. (C) 1998 Elsevier Science B.V.

关键词： feature detection multigrid algorithm corner detector

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Efficient Newton-Krylov solver for aerodynamic computations

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AIAA JOURNAL 1998年第11期36卷 1991-1997页

作者： Pueyo, A Zingg, DW Univ Toronto Inst Aerosp Studies Downsview ON M3H 5T6 Canada

An efficient inexact Newton-Krylov algorithm is presented for the computation of steady two-dimensional aerodynamic flows. The algorithm uses the preconditioned, restarted generalized minimal residual method in matrix-free form to solve the linear system arising at each Newton iteration. The preconditioner is formed using a block-fill incomplete lower-upper factorization of an approximate Jacobian matrix with two levels of fill after applying the reverse Cuthill-McKee reordering. The algorithm has been successfully applied to a wide range of test cases, which include inviscid, laminar, and turbulent aerodynamic flows. In all cases, convergence of the residual to 10(-12) is achieved with a computing cost equivalent to fewer than 1000 function evaluations. The matrix-free inexact Newton-Krylov algorithm is shown to converge faster and more reliably than an approximate Newton algorithm and an approximately factored multigrid algorithm.

关键词： multigrid algorithm Computing Cost multigrid Methods RAE Airfoil High Aspect Ratio Biconjugate Gradient Eddy Viscosity Computing Navier Stokes Equations Gaussian Elimination

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multigrid algorithm FOR 3-DIMENSIONAL INCOMPRESSIBLE HIGH-REYNOLDS NUMBER TURBULENT FLOWS

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AIAA JOURNAL 1995年第11期33卷 2073-2079页

作者： SHENG, CH TAYLOR, LK WHITFIELD, DL Mississippi State University Mississippi State Mississippi 39762

In this paper, a robust multigrid algorithm is presented for solving three-dimensional incompressible high-Reynolds number turbulent hows on high aspect ratio grids. The artificial compressibility form of the Navier-Stokes equations is discretized in a cell-centered finite volume form on a time-dependent curvilinear coordinate system, and the so-called discretized Newton-relaxation scheme is used as the iterative procedure for the solution of the system of equations. A nonlinear multigrid scheme (full approximation scheme [FAS]) is applied to accelerate the convergence of the time-dependent equations to a steady state. Two methods for constructing the coarse grid operator, the Galerkin coarse grid approximation and the discrete coarse grid approximation have also been investigated and incorporated into the FAS. A new procedure, called implicit correction smoothing that leads to high efficiency of the multigrid scheme by allowing large Courant-Friedrichs-Lewy numbers, is introduced in this work. Numerical solutions of high-Reynolds number turbulent bows for practical engineering problems are presented to illustrate the efficiency and accuracy of the current multigrid algorithm.

关键词： multigrid algorithm Freestream Velocity Incompressible Flow Total Variation Diminishing High Aspect Ratio Navier Stokes Equations Velocity Profiles Curvilinear Coordinates multigrid Methods Angle of Attack

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Mass-flux-based implicit multigrid method for modeling multidimensional combustion

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JOURNAL OF PROPULSION AND POWER 1997年第1期13卷 97-108页

作者： Zheng, XQ Liao, CM Liu, ZN Liu, CQ UNIV COLORADO DEPT MATH DENVER CO 80217 USA

A highly accurate and efficient method for modeling three-dimensional reacting flows with detailed chemistry is described in this paper, A mass-flux-based governing system is developed for general curvilinear coordinates to obtain compactness of the discretization stencil. The momentum equations are represented by a set of equations of mass fluxes across cell interfaces, which are discretized by using staggered grid techniques, A third-order monotone upwind-biased scheme is used for all of the convection terms in the flow equations and species equations to minimize numerical diffusion and capture the sharp gradients existing in flames, The governing equations are divided into a chemical reaction part and a fluid now part, and they are solved in a semicoupled way, An implicit semicoarsening multigrid method combined with a line-distributive relaxation is used as the how solver, The species equations are discretized by an implicit method and solved in a fully coupled way, Computational results for a confined coflowing diffusion name show good agreement with experimental data, A detailed three-dimensional calculation of combustion in a gas-turbine combustor with strong swirling inflows is also presented.

关键词： multigrid Methods Prandtl Numbers Curvilinear Coordinates Gas Turbine Combustor Mass Flux Direct Numerical Simulation Conservation Equations Combustors multigrid algorithm Turbulent Combustion

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The communication performance of the Cray T3D and its effect on iterative solvers

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PARALLEL COMPUTING 1996年第6期22卷 829-844页

作者： Hu, YF Emerson, DR Blake, RJ Daresbury Laboratory CLRC Warrington WA4 4AD United Kingdom

On many distributed memory systems, such as workstation clusters or the Intel iPSC/860, the multigrid algorithm suffers from having extensive communication requirements and, in general, it is not very competitive in comparison to the conjugate gradient algorithm. This is in contrast to the sequential problem whereby the multigrid algorithm is very effective in reducing the global residual, particularly for very large linear systems of equations. These two algorithms are now compared on the Gray T3D for solving very large systems of linear equations (resulted from grids of the order 256(3) cells). The communication performance of the Gray T3D is first measured by the standard ping-pong tests and also by practical communication tasks that are found frequently in CFD calculations. It is found that the Gray no has a low latency (approximate to 6 mu s) and a high bandwidth interprocessor communication (120 MB/s) when the low-level intrinsic communication routines are used. As a result, the multigrid algorithm is found to be very competitive when compared with the conjugate gradient algorithm for solving the very large linear systems arising from the Direct Numerical Simulation of turbulent Combustion (DNSC). Results are contrasted by those on the Intel iPSC/860.

关键词： distributed memory system communication requirements multigrid algorithm Computational Fluid Dynamics (CFD) Cray T3D iterative solvers

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Three-dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations

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AIAA JOURNAL 1996年第2期34卷 281-290页

作者： Braaten, ME Connell, SD General Electric Research and Development Center Schenectady New York 12301

A solution adaptive multigrid scheme for solving the three-dimensional Navier-Stokes equations on unstructured meshes is presented. The algorithm solves the equations on a fully unstructured mesh of tetrahedral elements, using a multigrid time-marching scheme. The initial unstructured mesh is successively refined based on gradients in the flow solution, with the multigrid levels being determined by the refinement procedure. Important issues related to solving viscous flows on unstructured meshes are discussed, These include calculation of the viscous stress terms in a manner that prevents wiggles, calculation of the time steps to include both inviscid and viscous effects, numerical smoothing considerations, minimization of computer storage requirements, and implementation of the k-epsilon turbulence model. Solutions are presented for several examples of industrial importance that illustrate the potential of the method, including transonic flow about an aircraft engine nacelle, and in both rotating and nonrotating turbomachinery passages.

关键词： Navier Stokes Equations Transonic Flow Nacelles Turbomachinery Tetrahedral Element Turbulence Models Freestream Mach Number Courant Friedrichs Lewy Unstructured Grid multigrid algorithm

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COARSE GRID CORRECTION SCHEME FOR IMPLICIT MULTIBLOCK EULER CALCULATIONS

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AIAA JOURNAL 1995年第10期33卷 1816-1821页

作者： JENSSEN, CB WEINERFELT, PA SINTEF FDN SCI & IND RESN-7034 TRONDHEIMNORWAY LINKOPING UNIV INST APPL MATHS-58183 LINKOPINGSWEDEN

A coarse grid correction scheme is used to bring global influence to implicit multiblock calculations. Compared to using only explicit coupling between the blocks, a considerable reduction in the number of time steps needed to reach steady state has been observed for transonic and subsonic flows. The additional CPU time per time step associated with the method is small, resulting in a highly efficient parallel implicit scheme.

关键词： Supersonic Flow Jacobi Method Delta Wing Angle of Attack Euler Equations Total Variation Diminishing Pressure Coefficient multigrid algorithm multigrid Methods Mach Numbers

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NAVIER-STOKES APPLICATIONS TO HIGH-LIFT AIRFOIL ANALYSIS

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JOURNAL OF AIRCRAFT 1995年第3期32卷 618-624页

作者： VALAREZO, WO MAVRIPLIS, DJ MCDONNELL DOUGLAS AEROSP LONG BEACHCA 90846

This article presents applications of a compressible Reynolds-averaged Navier-Stokes method to the calculation of flows about a transport-type multielement airfoil. The unstructured-mesh method used utilizes multigrid techniques for computational efficiency and includes a selection of turbulence models. The airfoil used to benchmark the computational capability is a three-element airfoil configured for landing for which extensive experimental data have been acquired both on and off the airfoil surface at high Reynolds numbers, Comparisons of computational results vs experimental data shown here include traditional airfoil performance calculations due to configuration changes. Also discussed are detailed comparisons of computational results and experimental data obtained in the flap well region to assess the applicability of existing turbulence models to the nap slot flow. Performance comparisons are conducted for configurations tested at chord Reynolds numbers of 5 x 10(6) and 9 x 10(6) and the flap well study is based on data obtained on a similar airfoil at a chord Reynolds number of 5 x 10(5).

关键词： Airfoil Surface Freestream Mach Number Spalart Allmaras Turbulence Model Reynolds Averaged Navier Stokes Lift Coefficient Flap Deflection Flow Conditions multigrid algorithm Unstructured Grid Wind Tunnel Tests

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3-DIMENSIONAL multigrid REYNOLDS-AVERAGED NAVIER-STOKES SOLVER FOR UNSTRUCTURED MESHES

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AIAA JOURNAL 1995年第3期33卷 445-453页

作者： MAVRIPLIS, DJ NASA Langley Research Center Hampton Virginia 23681

A three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes solver is described. Turbulence is simulated using a single field-equation model. Computational overheads are minimized through the use of a single edge-based data structure, an efficient multigrid solution technique, and the use of multitasking on shared memory multiprocessors. The accuracy and efficiency of the code are evaluated by computing two-dimensional flows in three dimensions and comparing with results from a previously validated two-dimensional code that employs the same solution algorithm. The feasibility of computing three-dimensional turbulent flows on grids of several million points in less than 2 h of wall clock time is demonstrated.

关键词： Reynolds Averaged Navier Stokes multigrid algorithm Three Dimensional Turbulent Flow Computing Aspect Ratio Flapping Wing RAE 2822 Eddy Viscosity Navier Stokes Equations Turbulence Models

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