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multigrid SOLUTION OF THE NAVIER-STOKES EQUATIONS ON TRIANGULAR MESHES

AIAA JOURNAL 1990年第8期28卷 1415-1425页

作者： MAVRIPLIS, DJ JAMESON, A PRINCETON UNIV DEPT MECH & AEROSP ENGNPRINCETONNJ 08544

A new 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 to 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, quadrilateralmesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Navier Stokes Equations NACA 0012 Finite Volume Approximation multigrid algorithm Laminar Boundary Layer Navier Stokes algorithm Freestream Mach Number Aspect Ratio Compressible Flow Computing

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DIAGONAL IMPLICIT multigrid algorithm FOR THE EULER EQUATIONS

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AIAA JOURNAL 1988年第7期26卷 841-851页

作者： CAUGHEY, DA Cornell University Ithaca New York

A multigrid implementation of the Alternating Direction Implicit algorithm has been developed to solve the Euler equations of in viscid, compressible flow. The equations are approximated using a finite-volume spatial discretization with added dissipation provided by an adaptive blend of second and fourth differences. For computational efficiency, the equations are diagonalized by a local similarity transformation so that only a decoupled system of scalar pentadiagonal systems need be solved along each line. Results are computed for transonic flows past airfoils and include pressure distributions to verify the accuracy of the basic scheme and convergence histories to demonstrate the efficiency of the method. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Continuity Equation multigrid algorithm Compressible Flow Freestream Mach Number Angle of Attack NACA 0012 High Aspect Ratio multigrid Methods Finite Volume Approximation Navier Stokes Equations

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LU IMPLICIT multigrid algorithm FOR THE 3-DIMENSIONAL EULER EQUATIONS

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AIAA JOURNAL 1988年第9期26卷 1061-1069页

作者： YOKOTA, JW CAUGHEY, DA NASA LEWIS RES CTRCLEVELANDOH 44135 CORNELL UNIV ITHACANY 14853

An LU implicit multigrid scheme is developed for the calculation of three-dimensional transonic flow through rotating cascades. This numerical method solves the unsteady Euler equations in finite-volume form with added adaptive artificial dissipation. The implicit scheme allows one to take a much larger time step than is normally permitted in most explicit schemes, while the multigrid method is incorporated to accelerate the convergence rate for steady-state calculations. Using this method, computational storage requirements are comparable to those of explicit schemes, while operation counts are considerably less than those found in the more widely used alternating direction implicit schemes. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Continuity Equation multigrid Methods Flow Conditions multigrid algorithm Mach Number NACA 0012 Finite Volume Formulation Compressor Rotors Static Pressure Flow Velocity

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DIAGONAL IMPLICIT multigrid CALCULATION OF INLET FLOWFIELDS

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AIAA JOURNAL 1989年第1期27卷 110-112页

作者： CAUGHEY, DA IYER, RK Cornell University Ithaca New York

A diagonal implicit multigrid algorithm to solve the Euler equations has been applied by D.A. Caughey to compute the transonic flow past a two-dimensional airfoil. It is the purpose of this note to describe an extensi... 详细信息

关键词： Compressible Flow Pressure Coefficient Continuity Equation multigrid Methods Freestream Mach Number Vortices multigrid algorithm Kinematic Viscosity

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COMPUTATIONS OF SUPERSONIC FLOWS OVER A BODY AT HIGH ANGLES OF ATTACK

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AIAA JOURNAL 1989年第4期27卷 427-437页

作者： BAYSAL, O FOULADI, K MILLER, DS NASA LANGLEY RES CTR SUPERSON HYPERSON AERODYNAM BRANCH HSAD HAMPTON VA 23665 USA

Three-dimensional supersonic flows over a blunt-nose-cylinder at 20, 32, and 44 deg angles of attack were computed. Length-to-diameter ratio of the cylinder used for the computations was 6.67 with a base diameter of 3 in. The flowfield was dominated by large-scale, multiple vortices generated by the crossflow separation. The mass averaged Navier-Stokes equations were solved by an approximately factored, upwind-biased, implicit, finite volume scheme. The Reynolds shear stress terms were modeled algebraically with modifications to correct the turbulent length and velocity scales in separated regions. The initializations of the flows were enhanced by a mesh sequencing strategy applied to the diagonalized form of the discretized equations. The convergence to steady-state was accelerated by a multigrid algorithm that used the block inversions for the discretized equations. Calculations were compared successfully with experimental results. © 1989 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Lift Coefficient Flow Conditions Karman Vortex Street Freestream Mach Number Reynolds Averaged Navier Stokes Compressibility multigrid algorithm Navier Stokes Calculations Finite Volume Formulation Shear Stress

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GORTLER INSTABILITY OF WALL JETS

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AIAA JOURNAL 1989年第1期27卷 112-114页

作者： FLORYAN, JM University of Western Ontario London Ontario Canada

Goertler instability of wall jet over a concave surface has been analyzed. The results suggest that the fundamental instability mode may have a form of one, two, and more layers of vortices, depending on the flow conditions. The unstable motion is expected to originate in the form of a single layer of vortices, which separates subsequently into two, three, or more distinct layers further downstream. The increased dissipation resulting from the vortex split phenomenon could lead to a self-stabilization of vortices of short wavelengths. The present analysis is based on a model rationally incorporating the effects of boundary-layer growth.

关键词： Vortices Gortler Numbers Blasius Boundary Layer Finite Volume Method Euler Equations Flow Conditions multigrid algorithm Kinematic Viscosity Shear Stress

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EXPLICIT multigrid algorithm FOR QUASI-3-DIMENSIONAL VISCOUS FLOWS IN TURBOMACHINERY

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JOURNAL OF PROPULSION AND POWER 1987年第5期3卷 397-405页

作者： CHIMA, RV NASA Lewis Research Center Cleveland Ohio

A rapid quasi-three-dimensional analysis has been developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin- Lomax eddy viscosity model is used for turbulent flows. The equations are solved using a two-stage Runge- Kutta scheme made efficient by the use of vectorization, a variable time step, and a flux-based multigrid scheme, all of which are described. Results of a stability analysis are presented for the two-stage scheme. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi-three-dimensional viscous analysis can be a practical design tool. © 1987 American Institute of Aeronautics and Astronautics, Inc.

关键词： Turbomachinery Design One Dimensional Flow multigrid algorithm Centrifugal Compressor Navier Stokes Equations Eddy Viscosity Mach Number Static Pressure Poisson's Equation Stagnation Region

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multigrid ACCELERATION OF THE FLUX-SPLIT EULER EQUATIONS

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AIAA JOURNAL 1988年第6期26卷 649-654页

作者： ANDERSON, WK THOMAS, JL WHITFIELD, DL MISSISSIPPI STATE UNIV DEPT AEROSP ENGNMISSISSIPPI STATEMS 39762

multigrid acceleration is applied to a flux-split algorithm for solving the Euler equations in three dimensions. The basic algorithm is an implicit spatially split approximate factorization method. The stability and performance of the scheme in comparison to other factorizations are examined. Results are presented for three-dimensional flows that demonstrate substantially unproved convergence with the multigrid algorithm. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Euler Equations multigrid algorithm Lift Coefficient Conservation of Mass multigrid Methods Supersonic Flow Freestream Mach Number Aspect Ratio NASA Langley Research Center Convection

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multigrid SOLUTION OF THE TWO-DIMENSIONAL EULER EQUATIONS ON UNSTRUCTURED TRIANGULAR MESHES

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AIAA JOURNAL 1988年第7期26卷 824-831页

作者： MAVRIPLIS, DJ NASA Langley Research Center Hampton Virginia

A multigrid algorithm has been developed to accelerate the convergence of the Euler equations to a steady state on unstructured triangular meshes. The method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes. A tree-search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells. The multigrid method is applied to two different discretizations of the Euler equations, and results about multi-element airfoils are presented. For both discretization schemes, convergence is accelerated by an order of magnitude, resulting in convergence rates comparable to those obtained with structured multigrid algorithms. © 1988 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Euler Equations multigrid algorithm Search algorithm multigrid Methods Drag Coefficient Bilinear Interpolation Triangular Element Leading Edge Slat Aspect Ratio Supercomputers

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SOR AND MGR[V] EXPERIMENTS ON THE CRYSTAL MULTICOMPUTER

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PARALLEL COMPUTING 1987年第2期4卷 117-142页

作者： KAMOWITZ, D Institute for Computer Applications in Science and Engineering ICASE NASA Langley Research Center Hampton VA 23665 U.S.A.

This report describes distributed implementations of the red/black SOR algorithm and of the MGR[ν] multigrid algorithm on the Crystal multicomputer. Rates of convergence and observed efficiencies for both algorithms ... 详细信息

关键词： Crystal multicomputer multigrid algorithm performance analysis SOR algorithm

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