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PARALLEL COMPUTING STRATEGIES FOR BLOCK multigrid IMPLICIT SOLUTION OF THE EULER EQUATIONS

AIAA JOURNAL 1992年第8期30卷 2032-2038页

作者： YADLIN, Y CAUGHEY, DA CORNELL UNIV CORNELL NATL SUPERCOMP FACILITHACANY 14853 CORNELL UNIV SIBLEY SCH MECH & AEROSP ENGNITHACANY 14853

A multigrid diagonal implicit algorithm has been developed to solve the three-dimensional Euler equations of inviscid compressible flow on block-structured grids. An improved method of advancing the multigrid cycle has been examined with respect to convergence rates, accuracy, and efficiency. In this method, the multigrid cycle is advanced independently in each of the blocks, and the information exchange between the blocks is done using buffer arrays, allowing for the asynchronous updating of interface boundary conditions. This updating scheme is used to eliminate the convergence problems found in a previous implementation of the algorithm while retaining its potential for efficient parallel execution. Results are computed for transonic flows past wings and include pressure distributions to verify the accuracy of the scheme and convergence histories to demonstrate the efficiency of the method. Efficiencies that were obtained using a modest number of processors in parallel are also presented and discussed.

关键词： Continuity Equation Compressible Flow Parallel Computing Strategies Aerodynamic Configurations Lift Coefficient multigrid algorithm FORTRAN Wind Tunnel Tests Mean Aerodynamic Chord Parallel Computers

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3-DIMENSIONAL UNSTRUCTURED multigrid FOR THE EULER EQUATIONS

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AIAA JOURNAL 1992年第7期30卷 1753-1761页

作者： MAVRIPLIS, DJ NASA Langley Research Center Hampton Virginia 23665

The three-dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady state of the fine grid solution. Variables, residuals, and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, whereas gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

关键词： Primitive Variable multigrid algorithm Linear Interpolation Galerkin Finite Element Approach Aeroplane Tetrahedral Element multigrid Methods Drag Coefficient Aircraft Configurations Unstructured Grid

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LOCAL SOLUTION ACCELERATION METHOD FOR THE EULER AND NAVIER-STOKES EQUATIONS

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AIAA JOURNAL 1992年第2期30卷 340-348页

作者： DRIKAKIS, D TSANGARIS, S NATL TECH UNIV ATHENS AERODYNAM LAB GR-147 ATHENS GREECE

The solution of the compressible Euler and Navier-Stokes equations via an upwind finite volume scheme is obtained. For the inviscid fluxes, the monotone upstream-centered scheme for conservation laws (MUSCL) has been incorporated into a Riemann solver. The MUSCL scheme is used for the unfactored implicit equations that are solved by a Newton form, and relaxation is performed via Gauss-Seidel relaxation technique. The solution on the fine grid is obtained by iterating first on a sequence of coarser grids and then interpolating the solution up to the next refined grid. Since the distribution of the numerical error is nonuniform, the local solution of the equations can be obtained in regions where the numerical errors are large. The construction of the partial meshes, in which the iterations will be continued, is determined by an adaptive procedure taking into account some convergence criteria. Reduction of the computational work units for two-dimensional problems is obtained via the local adaptive mesh solution which is expected to be more effective in three-dimensional complex flow computations.

关键词： Navier Stokes Equations Courant Friedrichs Lewy Finite Volume Scheme Compressible Fluid Euler Equations multigrid Methods Bilinear Interpolation Pressure Coefficient multigrid algorithm NACA 0012

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BLOCK multigrid IMPLICIT SOLUTION OF THE EULER EQUATIONS OF COMPRESSIBLE FLUID-FLOW

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AIAA JOURNAL 1991年第5期29卷 712-719页

作者： YADLIN, Y CAUGHEY, DA Cornell University Ithaca New York 14853

A multigrid diagonal implicit algorithm has been developed to solve the Euler equations of inviscid compressible flow on block structured grids. Two modes of advancing the multigrid cycle have been examined with respect to convergence rates, accuracy, and efficiency. The algorithm has been designed to run on parallel computers. Results are computed for transonic flows past airfoils and include pressure distributions to verify the accuracy of the scheme and convergence histories to demonstrate the efficiency of the method. Efficiencies that were obtained using a modest number of processors in parallel are presented and discussed.

关键词： Euler Equations Compressible Fluid Parallel Computers Lift Coefficient multigrid algorithm Freestream Mach Number NACA 0012 FORTRAN Poisson's Equation multigrid Methods

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multigrid AND UPWIND VISCOUS-FLOW SOLVER ON 3-DIMENSIONAL OVERLAPPED AND EMBEDDED GRIDS

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AIAA JOURNAL 1991年第6期29卷 903-910页

作者： BAYSAL, O FOULADI, K LESSARD, VR Old Dominion University Norfolk Virginia 23529

A computationally efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flows about complex configurations with geometrically nonsimilar components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually without significant restrictions. The Navier-Stokes equations are solved by an implicit, upwind, finite-volume scheme. The convergence is accelerated by a multigrid algorithm despite the holes created in the computational domain by the overlapped grids, which are completely or partially embedded within one another. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the existence of such holes. The method is tested through two demonstrative cases. The solution for a supersonic flow past a blunt-nose cylinder at a high angle of attack is obtained using a C-O grid embedded in a global Cartesian grid. This solution is successfully compared with the one obtained using a single C-O grid and the experimental data. Then, supersonic interference flows past an ogive-nose cylinder in the close proximity of a flat plate are solved using overlapped and topologically nonsimilar but simple grids.

关键词： Compressible Flow multigrid algorithm Angle of Attack Finite Volume Method Navier Stokes Equations Aerodynamic Interference Reynolds Averaged Navier Stokes Computational Fluid Dynamics Viscosity Domain Decomposition Methods

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ITERATIVE SOLUTION METHODS FOR PLATE BENDING PROBLEMS - multigrid AND PRECONDITIONED CG algorithm

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1990年第6期27卷 1450-1465页

作者： PEISKER, P RUST, W STEIN, E

The numerical solution of the linear equations arising from a discretization of the plate bending problem based on the Zienkiewicz triangle is studied. The finite element scheme proceeds from the Mindlin–Reissner formulation with modified shear energy. However, the Kirchhoff condition is imposed on discrete points. A multigrid algorithm is analyzed and numerical examples are provided. Furthermore, a suitable preconditioning is established for the use of conjugate gradients.

关键词： 65N30 multigrid algorithm preconditioned conjugate gradients Kirchhoff plate Mindlin–Reissner plate finite elements

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DIAGONAL INVERSION OF LOWER-UPPER IMPLICIT SCHEMES

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AIAA JOURNAL 1990年第2期28卷 263-266页

作者： YOKOTA, JW CAUGHEY, DA CHIMA, RV CORNELL UNIV SIBLEY SCH MECH & AEROSP ENGNITHACANY 14853 NASA LEWIS RES CTRCLEVELANDOH 44135

A new diagonally inverted lower-upper (LU) implicit scheme is developed for the three-dimensional Euler equations. The matrix systems that are to be inverted in the scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the diagonalized alternating direction implicit method, the time accuracy of the LU scheme is not reduced since the diagonalizing procedure does not destroy time conservation. Furthermore, this diagonalization reduces the computational effort required to solve the implicit approximation and therefore transforms it into a more efficient method of numerically solving the three-dimensional Euler equations. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Euler Equations multigrid Methods multigrid algorithm Transonic Flow Finite Volume Formulation Gaussian Elimination Fluid Density Total Energy

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NAVIER-STOKES COMPUTATIONS OF VORTICAL FLOWS OVER LOW-ASPECT-RATIO WINGS

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AIAA JOURNAL 1990年第2期28卷 205-212页

作者： THOMAS, JL KRIST, ST ANDERSON, WK VIGYAN RES ASSOCIATES INC HAMPTONVA

An upwind-biased finite-volume algorithm is applied to the low-speed laminar flow over a low-aspect-ratio delta wing from 0 to 40 deg angle of attack. The differencing is second-order accurate spatially and a multigrid algorithm is used to promote convergence to the steady state. The results compare well with the detailed experiments of Hummel and others for an Ret of 0.95 × 10⁶. The predicted maximum lift coefficient of 1.10 at 35 deg angle of attack agrees closely with the measured maximum lift of 1.06 at 33 deg. At 40 deg angle of attack, a bubble type of vortex breakdown is evident in the computations, extending from 0.6 of the root chord to just downstream of the trailing edge. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Low Aspect Ratio Wings Lift Coefficient Flap Deflection Vortex Breakdown Supersonic Flow Aspect Ratio multigrid algorithm Freestream Mach Number Adverse Pressure Gradient Shear Stress

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DIAGONALLY INVERTED LOWER-UPPER FACTORED IMPLICIT multigrid SCHEME FOR THE 3-DIMENSIONAL NAVIER-STOKES EQUATIONS

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AIAA JOURNAL 1990年第9期28卷 1642-1649页

作者： YOKOTA, JW Sverdrup Technology Inc. NASA Lewis Research Center Group Cleveland Ohio 44135

A diagonally inverted, lower-upper, approximately factored, implicit multigrid algorithm is developed to calculate three-dimensional compressible viscous flows. This scheme solves the full Reynolds-averaged Navier-Stokes equations with a k-ε model of turbulence. The flow equations are solved within the framework of the multigrid method using a four grid level W-cycle, while the k-ε equations are solved only on the finest grid and uncoupled from the flow calculations. This treatment proves to be an efficient method for calculating three-dimensional compressible viscous flows. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Navier Stokes Calculations Reynolds Averaged Navier Stokes Velocity Profiles In Compressible Viscous Flows Continuity Equation multigrid Methods Cartesian Coordinate System multigrid algorithm Turbulence Kinetic Energy Turbulence Models

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ACCURATE multigrid SOLUTION OF THE EULER EQUATIONS ON UNSTRUCTURED AND ADAPTIVE MESHES

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AIAA JOURNAL 1990年第2期28卷 213-221页

作者： MAVRIPLIS, DJ NASA Langley Research Center Hampton Virginia

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid-refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Euler Equations Supercritical Flow multigrid algorithm Shear Layers Freestream Mach Number Reynolds Averaged Navier Stokes NACA 0012 Computing Angle of Attack Search algorithm

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