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Mean-flow-multigrid for implicit Reynolds-stress-model computations

AIAA JOURNAL 2005年第9期43卷 1887-1898页

作者： Gerolymos, GA Vallet, I Univ Paris 06 Lab Energet F-75252 Paris France

The purpose of this work is to develop an efficient and robust multigrid acceleration technique for the computation of the compressible Favre-Reynolds-averaged Navier-Stokes equations with seven-equation Reynolds-stressmodel turbulence closures. The basic monogrid algorithm uses an upwind-biased O(Delta x(3)) flux-vector-split space discretization with implicit time integration. The discrete system of nonlinear equations is solved by a subiterative procedure, based on a local dual-time-stepping technique, which includes quasi-Newton iteration in the limit Delta t -> infinity. Full-approximation scheme sawtooth cycle multigrid is applied on the mean-flow variables only, while turbulence variables are simply injected into coarser grids. Characteristic-based multigrid is used for the restriction operator. The straightforward extension of the method to lower-level two-equation k-epsilon closures is described: Computational examples for various two- and three-dimensional complex flows, including large separation and/or shock-wave/boundary-layer interactions using different turbulence models, demonstrate that speed-ups of 3 to 4 are obtained, using three levels of multigrid (fine + two coarser grids).

关键词： Reynolds Averaged Navier Stokes Kinematic Viscosity Turbulence Models Boundary Layer Interaction Shock Waves Nonlinear Equation Incompressible Flow multigrid algorithm Turbulence Kinetic Energy Mach Numbers

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Effect of afterbody configuration on damping coefficients for axisymmetric projectiles

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JOURNAL OF SPACECRAFT AND ROCKETS 2004年第6期41卷 1065-1068页

作者： Park, SH Kwon, JH Korea Adv Inst Sci & Technol Dept Aerosp Engn Taejon 305701 South Korea

A prediction method for the pitch-damping coefficients was presented in the unified framework of the turbulent Navier-Stokes equations. Using the relative velocities of the coning motions in the unsteady governing equations enables the prediction of the pitch-damping coefficients in a simple manner. The present methods were applied to predict the static aerodynamic coefficients and the pitch-damping coefficients for the SOC configurations with different afterbody configurations. The results show that the flowfields due to the afterbody geometries affect the pitching and pitch-damping moments.

关键词： Damping Coefficient Projectiles Aerodynamic Coefficients Angle of Attack Supersonic Viscous Flow Navier Stokes Equations multigrid algorithm Supersonic Speed Pressure Coefficient Euler Equations

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multigrid algorithm for computing hypersonic, chemically reacting flows

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JOURNAL OF SPACECRAFT AND ROCKETS 2001年第6期38卷 865-874页

作者： Kim, SS Kim, C Rho, OH Seoul Natl Univ Dept Aerosp Engn Seoul 151742 South Korea

A robust and efficient multigrid method for computing inviscid and viscous high-speed steady-state reactive flows is presented. Curve-fitted data are used to calculate equilibrium properties. Nonequilibrium flows are calculated using five-species and two-temperature air models. The advection upstream splitting method by pressure-based weight functions is used to acquire robustness and spatial accuracy in capturing a shock and resolving a boundary layer. The five-stage Runge-Kutta and lower-upper symmetric Gauss-Seidel schemes are adopted for efficient time integration. The chemical source terms are treated in a point-implicit manner when five-stage Runge-Kutta is used. To overcome the stability problem in applying the multigrid method to high-speed reactive flow calculations, a modified damped prolongation and a new implicit residual smoothing are proposed. The proposed methods are applied to the computations of hypersonic equilibrium and nonequilibrium flows over a half-cylinder. The results reveal the robustness of the proposed methods and substantial multigrid speed-ups in both the equilibrium and nonequilibrium test cases.

关键词： Computing multigrid algorithm multigrid Methods Boundary Layer Chemically Reacting Flow Advection Total Variation Diminishing Freestream Conditions Prandtl Number Stagnation Streamlines

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Prediction of damping coefficients using the unsteady Euler equations

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JOURNAL OF SPACECRAFT AND ROCKETS 2003年第3期40卷 356-362页

作者： Park, SH Kim, Y Kwon, JH Korea Adv Inst Sci & Technol Dept Aerosp Engn Yuseong Gu Taejon 305701 South Korea

A prediction method for dynamic damping coefficients using the unsteady Euler equations is presented. Direct unsteady simulation can be used to compote the pitch-damping moment without any geometric approximations when compared to the steady methods using the coning motions. A forced harmonic pitching motion is employed to generate the pitch-damping moments. To compute the pitch- and the roll-damping moments for the basic finner, a dual-time stepping algorithm combined with an implicit multigrid method is applied. The computed coefficients show good agreement with the experimental data. Grid refinement and parametric studies are performed to assess the accuracy of the numerical method. The linearity of the angular rates and the variation with Mach numbers are examined for both pitch- and roll-damping moment coefficients. Through analysis of the pressure distributions at various Mach numbers, the large variations of roll-damping moment coefficient in the transonic region are explained in detail.

关键词： Euler Equations Damping Coefficient Freestream Conditions Angle of Attack Projectiles Hysteresis Loops Oblique Shock multigrid Methods multigrid algorithm Normal Shock Wave

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Computation of transonic diffuser flows by a lagged k-ω turbulence model

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JOURNAL OF PROPULSION AND POWER 2003年第3期19卷 473-483页

作者： Xiao, Q Tsai, HM Liu, F Natl Univ Singapore Temasek Labs Singapore 119260 Singapore Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92697 USA

The lag model proposed by Olsen and Coakley is applied in combination with the baseline k-omega two-equation turbulence model to simulate the steady and unsteady transonic flows in a diffuser. A fully implicit time-accurate multigrid algorithm is used to solve the unsteady Navier-Stokes equations and the coupled k-omega turbulence model equations. Two test cases are investigated, one with a weak shock in the channel corresponding to an exit-static-to-inlet-total pressure ratio Rp = 0.82 and the other with a strong shock corresponding to Rp = 0.72. Unsteady flows are induced by imposing fluctuating backpressure. Computational results are compared with experimental data and demonstrate notable improvement by the lag model for flows with strong shock-boundary-layer interactions.

关键词： Turbulence Models Supersonic Diffusers Compressibility Static Pressure Navier Stokes Equations Reynolds Stress multigrid algorithm multigrid Methods Courant Friedrichs Lewy Shear Stress

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Time-accurate inlet and outlet conditions for unsteady transonic channel flow

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AIAA JOURNAL 2002年第9期40卷 1745-1754页

作者： Ballmann, J Britten, G Sofronov, I Rhein Westfal TH Aachen Fac Math Informat & Sci Lehr & Forshcungsgebiet Mech D-52062 Aachen Germany Russian Acad Sci Dept Math Appl Keldysh Inst Appl Math Moscow 125047 Russia

Nonlocal inlet and outlet transparent boundary conditions (TBCs) based on a linear model of the Enter equations outside the computational domain are studied. The conditions are tested for both stationary and nonstationary flow problems about an airfoil in the numerical wind tunnel. Comparison is made with characteristic-based boundary conditions (CBCFs). Test calculations show that TBCs require much smaller computational domains for solving the problem. Unsteady calculations for the oscillating airfoil show that the solutions obtained with TBCs and CBCFs can strongly differ from each other in the case of certain resonance frequencies. In contrast to CBCFs, TBCs permit us to observe much better coincidence of solutions while increasing the size of the computational domains used. It is also observed that calculations for resonance cases require greater computational domains (up-and downstream) and much more oscillating cycles to obtain a periodical solution.

关键词： Wind Tunnel Tests Airfoil Channel Flow Euler Equations Resonance Frequencies Angle of Attack Reynolds Averaged Navier Stokes Mach Number multigrid algorithm Runge Kutta Methods

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Edge-based multigrid and preconditioning for hybrid grids

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AIAA JOURNAL 2002年第10期40卷 1954-1960页

作者： Moinier, P Müller, JD Giles, MB Univ Oxford Comp Lab Oxford OX1 3QD England Queens Univ Belfast Sch Aeronaut Engn Belfast BT9 5AG Antrim North Ireland

A multigrid method has been developed for the Euler and Navier-Stokes equations on unstructured hybrid grids in two and three dimensions. The coarse grids are automatically generated from the finest grid through element collapsing. This has been used in preference to a previous edge-collapsing technique to preserve as much structure as possible within semistructured grids. The performance of the multigrid is significantly improved through the use of Jacobi preconditioning within a Runge-Kutta iterative smoother. Results are presented for a variety of two-dimensional and three-dimensional problems, both inviscid and viscous, with the Spalart-Allmaras turbulence model.

关键词： Navier Stokes Calculations Spalart Allmaras Turbulence Model multigrid Methods Reynolds Averaged Navier Stokes multigrid algorithm High Aspect Ratio Freestream Conditions Euler Equations Business Jet Wing Tip

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Detachment of the dynamic-stall vortex above a moving surface

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AIAA JOURNAL 2002年第9期40卷 1811-1822页

作者： Obabko, AV Cassel, KW IIT Mech Mat & Aerosp Engn Dept Chicago IL 60616 USA

Dynamic stall occurs on helicopter blades and pitching airfoils when the dynamic-stall vortex, which forms as a result of an unsteady boundary-layer eruption near the leading edge, detaches from the surface and convects into the wake of the airfoil. The dynamic-stall vortex is modeled as a thick - core vortex above an infinite plane surface. Numerical solutions of the unsteady Navier-Stokes equations are obtained to determine the nature of the unsteady separation and vortex detachment processes and the influence of a moving wall. Whereas the unsteady separation process evolves very differently within two Reynolds number regimes, the detachment process is observed to be very similar over the range of Reynolds numbers considered. A moving wall has a significant influence on both processes. It is found that increasing the wall speed toward a critical value, which is equal to the magnitude of the maximum inviscid velocity at the surface, results in solutions that are indicative of flows at lower Reynolds numbers. Eventually, for wall speeds close to this critical value, formation of the recirculation region and unsteady separation are suppressed altogether, and detachment of the vortex is prevented.

关键词： Vortices Freestream Velocity Adverse Pressure Gradient Mixed Convection Boundary Layer Equations Poisson's Equation Navier Stokes Calculations multigrid algorithm Angle of Attack Characteristic Velocity

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On the effects of the temperature profile approximation in thermal Newtonian solutions of elastohydrodynamic lubrication line contacts

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART J-JOURNAL OF ENGINEERING TRIBOLOGY 2001年第J1期215卷 109-120页

作者： Kazama, T Ehret, P Taylor, CM Muroran Inst Technol Dept Mech Syst Engn Muroran Hokkaido 0508585 Japan Univ Leeds Sch Mech Engn Inst Tribol Leeds W Yorkshire England

The assumptions of a quadratic temperature profile and mean viscosity across the film, which are frequently used in the analysis of thermal elastohydrodynamic lubrication (EHL), are examined acid discussed. Two different approaches for solving the thermal EHL problem are compared for line contact conditions, namely (a) a one-dimensional model based upon both the assumption of a quadratic temperature profile and the adoption of the mean physical properties across the film and (b) a two-dimensional model which includes changes in temperature and physical properties of a lubricant across the film and which takes into account the conditions of reverse flow and heat convection across the film occurring at the inlet region. A multi-grid algorithm is implemented to solve these two conditions. The temperature profile and the general solutions in the conjunction obtained in both approaches are compared. For the one-dimensional model, results reveal that temperature peaks just prior to the inlet of the conjunction. This feature is not apparent in the two-dimensional model and results in lower values in film thickness and larger frictional coefficients than in the two-dimensional model. In the high-pressure region, both equations yield almost the same mean temperature.

关键词： elastohydrodynamic lubrication thermal elastohydrodynamic lubrication quadratic temperature profile multigrid algorithm energy equation

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A domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshes

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2001年第6期37卷 625-656页

作者： Dolean, V Lanteri, S INRIA Sophia Antipolis Project Sinus F-06902 Sophia Antipolis France

We report on our recent efforts on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two-dimensional compressible inviscid flows. The starting point is a flow solver for the Euler equations, which is based on a mixed finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is obtained using a linearized backward Euler implicit scheme. As a result, each pseudo-time step requires the solution of a sparse linear system for the flow variables. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. First, we formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces. In accordance with the hyperbolic nature of the Euler equations, these transmission conditions are Dirichlet conditions for the characteristic variables corresponding to incoming waves. Then. we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In our approach, the interface unknowns are numerical (normal) fluxes. Copyright (C) 2001 John Wiley & Sons, Ltd.

关键词： domain decomposition method Euler equations finite elements finite volumes multigrid algorithm parallel computing triangular meshes

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