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AGGLOMERATION multigrid FOR THE 3-DIMENSIONAL EULER EQUATIONS

AIAA JOURNAL 1995年第4期33卷 633-640页

作者： VENKATAKRISHNAN, V MAVRIPLIS, DJ NASA Langley Research Center Hampton VA 23681

A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the three-dimensional Euler equations on unstructured grids about complex configurations. It is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratios of the coarse grid cells. The agglomeration is done as a preprocessing step and runs in linear time. The implications for multigrid of using arbitrary polyhedral coarse grids are discussed. The agglomeration multigrid technique compares very favorably with existing multigrid procedures both in terms of convergence rates and elapsed times. The main advantage of the present approach is the ease with which coarse grids of any desired degree of coarseness may be generated in three dimensions, without being constrained by considerations of geometry. Inviscid flows over a variety of complex configurations are computed using the agglomeration multigrid strategy.

关键词： Euler Equations Aspect Ratio Two Dimensional Flow Unstructured Grid multigrid algorithm Freestream Mach Number Angle of Attack Piecewise Constant Interpolation Roe Approximate Riemann Solver Fuselages

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DESIGN AND IMPLEMENTATION OF A PARALLEL UNSTRUCTURED EULER SOLVER USING SOFTWARE PRIMITIVES

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AIAA JOURNAL 1994年第3期32卷 489-496页

作者： DAS, R MAVRIPLIS, DJ SALTZ, J GUPTA, S PONNUSAMY, R NASA LANGLEY RES CTRINST COMP APPLICAT SCI & ENGNHAMPTONVA 23665

This paper is concerned with the implementation of a three-dimensional unstructured-grid Euler solver on massively parallel distributed-memory computer architectures. The goal is to minimize solution time by achieving high computational rates with a numerically efficient algorithm. An unstructured multigrid algorithm with an edge-based data structure has been adopted, and a number of optimizations have been devised and implemented to accelerate the parallel computational rates. The implementation is carried out by creating a set of software tools, which provide an interface between the parallelization issues and the sequential code, while providing a basis for future automatic run-time compilation support. Large practical unstructured grid problems are solved on the Intel iPSC/860 hypercube and Intel Touchstone Delta machine. The quantitative effects of the various optimizations are demonstrated, and we show that the combined effect of these optimizations leads to roughly a factor of 3 performance improvement. The overall solution efficiency is compared with that obtained on the Cray Y-MP vector supercomputer.

关键词： multigrid algorithm Unstructured Grid Vector Supercomputers Software Tool Aircraft Configurations Molecular Dynamics Annealing Navier Stokes Solver Data Store FORTRAN

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PARALLELIMPLICIT UNSTRUCTURED GRID EULER SOLVERS

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AIAA JOURNAL 1994年第10期32卷 1985-1991页

作者： VENKATAKRISHNAN, V Institute for Computer Applications in Science and Engineering Hampton Virginia 23681

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

关键词： Unstructured Grid Parallel Computers Two Dimensional Flow Euler Equations Finite Volume Scheme multigrid algorithm Courant Friedrichs Lewy Roe Approximate Riemann Solver Navier Stokes Equations Angle of Attack

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APPLICATION OF THE multigrid SOLUTION TECHNIQUE TO HYPERSONIC ENTRY VEHICLES

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JOURNAL OF SPACECRAFT AND ROCKETS 1994年第5期31卷 744-750页

作者： GREENE, FA NASA Langley Research Center Hampton Virginia 23681

multigrid techniques have been incorporated into an existing hypersonic now analysis code, the Langley aerothermodynamic upwind relaxation algorithm. The multigrid scheme is based on the full approximation storage approach and uses full multigrid to obtain a well-defined fine-mesh starting solution. Predictions were obtained using standard transfer operators, and a V cycle was used to control grid sequencing. Computed hypersonic now solutions, compared with experimental data for a 15-deg blunted sphere-cone and a blended-wing body, are presented. It is shown that the algorithm predicts heating rates accurately, and computes solutions in one-third the computational time of the nonmultigrid algorithm.

关键词： Blended Wing Body Nonequilibrium Flows Aspect Ratio Aerothermodynamics Lift Coefficient Heat Transfer Measurements Freestream Mach Number multigrid algorithm Vortices Perfect Gas

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EFFICIENT CELL-VERTEX UPWIND SCHEME FOR THE 2-DIMENSIONAL EULER EQUATIONS

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AIAA JOURNAL 1994年第2期32卷 278-284页

作者： ROSSOW, CC Deutsche Forschungsanstalt fur Luft- und Raumfahrt Braunschweig D-38108 Germany

The accuracy and efficiency of a cell-vertex upwind scheme are investigated. Upwinding is achieved by an unequal distribution of the transformed flux balances to the vertices of a computational cell. The equations are rotated with respect to the local velocity vector to determine the upwinding directions. Fourth differences background dissipation is added to ensure convergence, and time integration is performed using a five-stage Runge-Kutta scheme. The background dissipation is scaled by the appropriate eigenvalues, and convergence toward steady state is accelerated by employing upwind implicit residual smoothing and multigrid. The scheme is second order accurate in space at steady state, and it yields very accurate results on significantly coarse meshes. Thus its efficiency is competitive with that of central-differencing schemes using multigrid acceleration.

关键词： Upwind Scheme Euler Equations Supersonic Flow multigrid algorithm Flow Velocity NACA 0012 Viscosity Bilinear Interpolation Numerical Integration Freestream Conditions

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FAST multigrid METHOD FOR SOLVING INCOMPRESSIBLE HYDRODYNAMIC PROBLEMS WITH FREE SURFACES

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AIAA JOURNAL 1994年第6期32卷 1175-1185页

作者： FARMER, J MARTINELLI, L JAMESON, A Princeton University Princeton New Jersey 08544

The focus of this work is the development of a finite-volume multigrid Euler scheme for solving three-dimensional, fully nonlinear ship wave problems. The flowfield and the a priori unknown free surface location are calculated by coupling the free surface kinematic and dynamic equations with the equations of motion for the bulk flow. The evolution of the free surface boundary condition is linked to the evolution of the bulk now via a novel iteration strategy that allows temporary leakage through the surface before the solution is converged. The method of artificial compressibility is used to enforce the incompressibility constraint for the bulk flow. A multigrid algorithm is used to accelerate convergence to a steady state. The scheme is validated by comparing the numerical results with experimental results for the Wigley parabolic hull. Waterline profiles from bow to stern are in excellent agreement with the experimental results. The computed wave drag compares favorably with both theory and experiment for a wide range of Froude numbers. Overall, the present method proves to be accurate and efficient.

关键词： Freestream Velocity Flow Characteristics Static Pressure multigrid Methods multigrid algorithm Incompressible Flow Finite Volume Scheme Continuity Equation Aerospace Engineering Navier Stokes Calculations

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A multigrid algorithm for parallel computers: CPMG

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Journal of Scientific Computing 1992年第3期7卷 263-279页

作者： Gupta, S.N. Zubair, M. Grosch, C.E. Old Dominion University Norfolk 23529-0162 Virginia United States

In this article, we present a multigrid algorithm for parallel computers, the chopped parallel multigrid (CPMG) algorithm. The CPMG algorithm improves the processor utilization by reducing the work load on coarse grids without affecting the convergence rate of the algorithm. This is in contrast to earlier approaches (Gannon and van Rosendale, 1986;Frederickson and McBryan, 1989), where unutilized processors are used to improve the convergence rate. The CPMG algorithm reduces the coarse grid work by chopping the alternate cycles of multigrid. Using analytical results and simulations on sequential machines we show that the CPMG can achieve almost the same convergence rate as standard MG for many cases. Analytically we show that the advantage gained by CPMG over standard MG on a mesh connected massively parallel machine is 33% in hardware utilization, 50% in communication overheads and 38% in overall execution time. We have also evaluated the performance of CPMG on an actual massively parallel machine, the DAP-510. The advantage gained by CPMG over standard MG is 35% in overall execution time. Moreover, the CPMG can be integrated with other parallel multigrid algorithms, such as the PSMG algorithm (Frederickson and McBryan, 1989) and Decker's algorithm (Decker, 1990). © 1992 Plenum Publishing Corporation.

关键词： multigrid algorithm Numerical methods parallel algorithms

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PRESSURE-BASED multigrid algorithm FOR FLOW AT ALL SPEEDS

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AIAA JOURNAL 1992年第11期30卷 2660-2669页

作者： SHYY, W CHEN, MH SUN, CS NATL CHENG KUNG UNIV INST AERONAUT & ASTRONAUTTAINANTAIWAN

A full multigrid/full approximation storage (FMG/FAS) method is developed along with a unified pressure-based algorithm to handle the complex fluid now problems encompassing both compressible and incompressible regimes. Besides highlighting the key elements of the present algorithm on a curvilinear staggered grid system, several flow problems, ranging from incompressible to hypersonic speeds, are computed, in conjunction with an adaptive grid method, to demonstrate its computational capability. With wide variations in geometry, fluid physics, and grid distribution, speedup between the single- and multigrid procedures can be obtained. Because different pressure boundary conditions are needed for incompressible, subsonic, and supersonic inlet and outlet, the number of grid levels that can be effectively used by the present multigrid method appears now dependent;the implications of this observation are discussed.

关键词： Numerical Stability Supersonic Inlets multigrid algorithm Velocity Profiles Hypersonic Speed Incompressible Viscous Flow Mach Number Natural Convection Pressure Correction Method Continuity Equation

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multigrid TECHNIQUES FOR HYPERSONIC VISCOUS FLOWS

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AIAA JOURNAL 1993年第9期31卷 1729-1731页

作者： GRASSO, F MARINI, M Universita di Roma "La Sapienza" Rome 00184 Italy

In the present work a multigrid technique for viscous hypersonic flows has been developed. The technique is based on the FAS-FMG method and it uses a V-cycle strategy. Applications to hypersonic flows show that the grid transfer operators play a crucial role for the robustness and effectiveness of technique: 1) to inhibit upstream propagation of high-frequency disturbances, the prolongation operator must have a directionality character;2) the robustness of the algorithm is increased by direction-dependent implicit residual smoothing;and 3) in the presence of strong shock-wave boundary-layer interaction the convergence is affected by the development of the recirculation region.

关键词： Inviscid Hypersonic Flow Sensitivity Analysis Aspect Ratio Freestream Velocity Total Variation Diminishing Numerical Integration Boundary Integral Equation Laminar Turbulent Transition Navier Stokes Equations multigrid algorithm

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multigrid CALCULATIONS OF A JET IN CROSS-FLOW

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JOURNAL OF PROPULSION AND POWER 1992年第2期8卷 425-431页

作者： CLAUS, RW VANKA, SP UNIV ILLINOIS DEPT MECH & IND ENGNURBANAIL 61801

In order to assess accurately the standard k-epsilon model in a three-dimensional recirculating flow, a series of numerical calculations of a jet in a crossflow have been made employing progressively fine finite-difference meshes consisting of up to 2.4 million grid nodes. The discretized equations have been solved with a block-implicit multigrid algorithm that is observed to converge efficiently. The calculated velocity and turbulence fields are compared with experimental data. It is observed that the general features of the flow are well predicted, but there are appreciable discrepancies between measured and calculated values. Even with current fine resolution, the calculation cannot be said to be completely grid independent;however, the major disagreements are believed to result from the turbulence model.

关键词： Turbulence Models multigrid algorithm Turbulence Kinetic Energy Shear Layers Freestream Velocity Large Eddy Simulation Flow Distribution Vortices Peclet Numbers Continuity Equation

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