The Current Status of Unsteady CFD Approaches for Aerodynamic Flow Control

An overview of the current status of time dependent algorithms is presented. Special attention is given to algorithms used to predict fluid actuator flows, as well as other active and passive flow control devices. Capabilities for the next decade are predicted, and principal impediments to the progress of time-dependent algorithms are identified.

[1]  Juhani Pitkäranta,et al.  An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation , 1986 .

[2]  Jeff Cash,et al.  On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae , 1980 .

[3]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[4]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[5]  J. Deardorff A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[6]  A. Cain,et al.  NUMERICAL SIMULATION OF SYNTHETIC JET ACTUATORS , 1997 .

[7]  Thorwald Herbert,et al.  Disturbances produced by motion of an actuator , 1997 .

[8]  J. Butcher The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[9]  L. D. Krai,et al.  ACTIVE FLOW CONTROL APPLIED TO AN AIRFOIL , 1998 .

[10]  S. Osher,et al.  Triangle based adaptive stencils for the solution of hyperbolic conservation laws , 1992 .

[11]  Seifert Avi,et al.  Periodic Excitation for Jet Vectoring and Enhanced Spreading , 1999 .

[12]  Mehdi R. Khorrami,et al.  Time-Accurate Simulations and Acoustic Analysis of Slat Free Shear Layer , 2002 .

[13]  E. Süli,et al.  hp-finite element methods for hyperbolic problems , 1999 .

[14]  Franck Nicoud,et al.  An approach to wall modeling in large-eddy simulations , 2000 .

[15]  D. Gottlieb,et al.  A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy , 1999 .

[16]  M. Delanaye,et al.  Computation of high Reynolds number flows with an implicit quadratic reconstruction scheme on unstructured grids , 1997 .

[17]  Chi-Wang Shu,et al.  On a cell entropy inequality for discontinuous Galerkin methods , 1994 .

[18]  Dimitri J. Mavriplis,et al.  Transonic drag prediction using an unstructured multigrid solver , 2002 .

[19]  Kjell Gustafsson,et al.  Control Strategies for the Iterative Solution of Nonlinear Equations in ODE Solvers , 1997, SIAM J. Sci. Comput..

[20]  R Spalart Philippe,et al.  Young-Person''s Guide to Detached-Eddy Simulation Grids , 2001 .

[21]  W. K. Anderson,et al.  An implicit upwind algorithm for computing turbulent flows on unstructured grids , 1994 .

[22]  Boris Diskin,et al.  Distributed Relaxation for Conservative Discretizations , 2001 .

[23]  W. K. Anderson,et al.  Navier-Stokes Computations of Vortical Flows Over Low-Aspect-Ratio Wings , 1987 .

[24]  Jan Nordström,et al.  Boundary and Interface Conditions for High-Order Finite-Difference Methods Applied to the Euler and Navier-Stokes Equations , 1999 .

[25]  David W. Zingg,et al.  Aerodynamic computations using a higher-order algorithm , 1999 .

[26]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[27]  G. D. Byrne,et al.  VODE: a variable-coefficient ODE solver , 1989 .

[28]  M. Strelets Detached eddy simulation of massively separated flows , 2001 .

[29]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[30]  Mehdi R. Khorrami,et al.  Time-Accurate Simulations and Acoustic Analysis of Slat Free-Shear-Layer: Part II , 2001 .

[31]  Ivo Babuška,et al.  On the Rates of Convergence of the Finite Element Method , 1982 .

[32]  V. Vatsa,et al.  development of a multigrid code for 3-D Navier-Stokes equations and its application to a grid-refinement study , 1990 .

[33]  Shahyar Pirzadeh,et al.  Three-dimensional unstructured viscous grids by the advancing-layers method , 1996 .

[34]  Thomas W. Roberts,et al.  The Development of a Factorizable Multigrid Algorithm for Subsonic and Transonic Flow , 2001 .

[35]  Mehdi R. Khorrami,et al.  UNSTEADY FLOW COMPUTATIONS OF A SLAT WITH A BLUNT TRAILING EDGE , 2000 .

[36]  V. Venkatakrishnan,et al.  A UNIFIED MULTIGRID SOLVER FOR THE NAVIER-STOKES EQUATIONS ON MIXED ELEMENT MESHES , 1995 .

[37]  Philippe R. Spalart,et al.  Detached-Eddy Simulations Past a Circular Cylinder , 2000 .

[38]  David Sidilkover,et al.  Factorizable upwind schemes: the triangular unstructured grid formulation , 2001 .

[39]  Bertil Gustafsson,et al.  The convergence rate for difference approximations to general mixed initial boundary value problems , 1981 .

[40]  Rémi Abgrall,et al.  On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation , 1994 .

[41]  I. Wygnanski,et al.  Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation , 1993 .

[42]  Harold L. Atkins,et al.  QUADRATURE-FREE IMPLEMENTATION OF DISCONTINUOUS GALERKIN METHOD FOR HYPERBOLIC EQUATIONS , 1996 .

[43]  Timothy J. Barth,et al.  Recent developments in high order K-exact reconstruction on unstructured meshes , 1993 .

[44]  Timothy J. Barth,et al.  Numerical Methods for Gasdynamic Systems on Unstructured Meshes , 1997, Theory and Numerics for Conservation Laws.

[45]  Harold L. Atkins,et al.  Eigensolution analysis of the discontinuous Galerkin method with non-uniform grids , 2001 .

[46]  H. L. Atkins,et al.  High-order ENO methods for the unsteady compressible Navier-Stokes equations , 1991 .

[47]  David B. Goldstein,et al.  Two-Dimensional Synthetic Jet Simulation , 2002 .

[48]  I. Wygnanski,et al.  Delay of Airfoil Stall by Periodic Excitation , 1996 .

[49]  B. Strand Summation by parts for finite difference approximations for d/dx , 1994 .

[50]  Neeraj Sinha,et al.  Hybrid RANS-LES simulation of cavity flow fields with control , 2002 .

[51]  D. Mavriplis Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes , 1997 .

[52]  John L. Lumley,et al.  Flow over an obstacle emerging from the wall of a channel , 1996 .

[53]  I. Babuska,et al.  ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD , 1976 .

[54]  P. Frederickson,et al.  Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction , 1990 .

[55]  Kenji Takeda,et al.  Unsteady aerodynamics and aeroacoustics of a high-lift device configuration , 2002 .

[56]  A. Glezer,et al.  Vectoring and small-scale motions effected in free shear flows using synthetic jet actuators , 1997 .

[57]  M. Carpenter,et al.  Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .

[58]  W. H. Kirk And and Or , 1921 .

[59]  Dimitri J. Mavriplis,et al.  Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm , 2001 .

[60]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[61]  Hester Bijl,et al.  Time Integration Schemes for the Unsteady Navier-stokes Equations , 2001 .

[62]  Computations of compressible synthetic jet flows using multigrid/dual time stepping algorithm , 1999 .

[63]  Dimitri J. Mavriplis,et al.  Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows , 1998 .

[64]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[65]  Yen Liu,et al.  Quadratic reconstruction finite volume schemes on 3D arbitrary unstructured polyhedral grids , 1999 .

[66]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[67]  Miguel R. Visbal,et al.  Numerical investigation of synthetic-jet flowfields , 1999 .

[68]  W. Mulder A high-resolution Euler solver based on multigrid, semi-coarsening, and defective correction , 1992 .

[69]  An essentially non-oscillatory high-resolution Pade-type (ENO-Pade) scheme , 2000 .

[70]  Avi Seifert,et al.  Active control of separated flows on generic configurations at high Reynolds numbers , 1999 .

[71]  Jan Nordström,et al.  High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates , 2001 .

[72]  Paresh Parikh,et al.  Generation of three-dimensional unstructured grids by the advancing-front method , 1988 .

[73]  Peter W. Carpenter,et al.  NUMERICAL SIMULATION OF THE INTERACTION OF MEMS ACTUATORS AND BOUNDARY LAYERS , 2000 .

[74]  Dimitri J. Mavriplis,et al.  On Convergence Acceleration Techniques for Unstructured Meshes , 1998 .

[75]  Dimitri J. Mavriplis,et al.  Parallel Performance Investigations of an Unstructured Mesh Navier-Stokes Solver , 2000, Int. J. High Perform. Comput. Appl..

[76]  R. LeVeque Numerical methods for conservation laws , 1990 .

[77]  George Em Karniadakis,et al.  The Development of Discontinuous Galerkin Methods , 2000 .

[78]  Thomas J. R. Hughes,et al.  Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations , 1984 .

[79]  D V Maddalon,et al.  Transition Flight Experiments on a Swept Wing With Suction , 1989 .

[80]  Harold L. Atkins,et al.  A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems , 1993 .

[81]  Philip L. Roe,et al.  A space-time discontinuous galerkin method for the time-accurate numerical solution of hyperbolic conservation laws , 1995 .

[82]  Ivo Babuska,et al.  The p and h-p Versions of the Finite Element Method, Basic Principles and Properties , 1994, SIAM Rev..

[83]  D. Gottlieb,et al.  Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes , 1994 .

[84]  P. Spalart Strategies for turbulence modelling and simulations , 2000 .

[85]  Chung-Sheng Yao,et al.  Unsteady slat wake characteristics of a 2-D high-lift configuration , 2000 .

[86]  J. Lambert Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[87]  Dimitri J. Mavriplis,et al.  AIAA 99 – 0537 LARGE-SCALE PARALLEL UNSTRUCTURED MESH COMPUTATIONS FOR 3 D HIGH-LIFT ANALYSIS , 1999 .

[88]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[89]  Pierre Charrier,et al.  Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws , 2001 .

[90]  P. Olsson Summation by parts, projections, and stability. II , 1995 .

[91]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[92]  Avi Seifert,et al.  Separation Control at Flight Reynolds Numbers: Lessons Learned and Future Directions , 2000 .

[93]  David W. Zingg,et al.  Higher-order aerodynamic computations on multi-block grids , 2001 .

[94]  S. Osher,et al.  Some results on uniformly high-order accurate essentially nonoscillatory schemes , 1986 .

[95]  A. Seifert,et al.  Oscillatory Control of Separation at High Reynolds Numbers , 1999 .

[96]  Sukumar Chakravarthy,et al.  Sub-grid turbulence modeling for unsteady flow with acoustic resonance , 2000 .

[97]  Strategies for turbulence modelling and simulations , 2000 .

[98]  Carl Ollivier-Gooch,et al.  High-order ENO schemes for unstructured meshes based on least-squares reconstruction , 1997 .

[99]  Florian,et al.  Improved Two-Equation k- Turbulence Models for Aerodynamic Flows , 2022 .

[100]  M. Delanaye,et al.  DEVELOPMENT AND APPLICATION OF QUADRATIC RECONSTRUCTION SCHEMES FOR COMPRESSIBLE FLOWS ON UNSTRUCTURED ADAPTIVE GRIDS , 1997 .

[101]  Timothy J. Barth,et al.  Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension , 2000 .

[102]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[103]  N. Frink Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows , 1996 .

[104]  J. Verwer,et al.  Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations , 1984 .

[105]  Lloyd N. Trefethen,et al.  How Fast are Nonsymmetric Matrix Iterations? , 1992, SIAM J. Matrix Anal. Appl..

[106]  Philippe R. Spalart,et al.  Detached-Eddy Simulations Over a Simplified Landing Gear , 2002 .

[107]  John C. Butcher,et al.  Diagonally-implicit multi-stage integration methods , 1993 .

[108]  R. C. Swanson,et al.  TOWARDS OPTIMAL MULTIGRID EFFICIENCY FOR THE NAVIER-STOKES EQUATIONS , 2001 .

[109]  Avi Seifert,et al.  Oscillatory Excitation of Unsteady Compressible Flows over Airfoils at Flight Reynolds Numbers , 1999 .

[110]  Ahmed A. Hassan,et al.  Effects of Zero-Mass “Synthetic” Jets on the Aerodynamics of the NACA-0012 Airfoil , 1998 .

[111]  D. Bonhaus,et al.  A higher order accurate finite element method for viscous compressible flows , 1999 .

[112]  H. Kreiss,et al.  Comparison of accurate methods for the integration of hyperbolic equations , 1972 .

[113]  R. Hoeld,et al.  Numerical Simulation of Aeroacoustic Sound Generated by Generic Bodies Placed on a Plate : Part-I, Prediction of Aero Acoustic Sources , 1999 .

[114]  Charles Hirsch,et al.  Numerical computation of internal and external flows (vol1: Fundamentals of numerical discretization) , 1991 .