Eli Turkel
Professor, Department of Applied Mathematics
Tel Aviv University

Numerical Methods for PDE's
and Computational Fluid Dynamics

Brief Research Summary

Over the recent years, the research has primarily focused on developing the numerical algorithms for solving the steady state compressible Navier-Stokes equations over aerodynamic bodies. The major area of applications consists of external flow problems. One of the main focuses has been on methods to accelerate the convergence to a steady state. We have been concentrating on low speed flows and have introduced preconditioning techniques to improve both the convergence rate and the accuracy of the resultant steady state.

Overview of Preconditioning
  • PRECONDITIONING

    Selected Publications

  • V.N. Vatsa and E. Turkel Synthetic Jet
    Simulation of Synthetic Jets Using Unsteady Reynolds-Averaged Navier-Stokes Equations
    AIAA Journal, 44:217-224, 2006
  • E. Turkel and V.N. Vatsa ESAIM
    Mathematical Modeling and Numerical Analysis
    ESAIM: M2AN 39 no. 3, 515-536, 2005
  • E. Turkel and V.N. Vatsa Porquerolles
    Local Preconditioners for Steady and Unsteady Flow Applications
    Conference on Low Mach Flows, Porquerolles, France, June 2004
  • V.N. Vatsa and E. Turkel Portland
    Assessment of Local Preconditioners for Steady State and Time Dependent Flows
    34th AIAA Fluid Dynamics Conference, Portland, OR AIAA paper 2004-2134, 2004
  • V.N. Vatsa and E. Turkel Orlando
    Choice of Variables and Preconditioning for Time Dependent Problems
    AIAA 16th Computational Fluid Dynamics Conference, Orlando, AIAA paper 2003-3692 CP, 2003.
  • V.N. Vatsa and E. Turkel viscous
    Robust Low Speed Preconditioning for Viscous High Lift Flows
    AIAA 40th Aerospace Sciences Meeting, Reno AIAA paper 2002-0962, 2002.
  • Celestina and Turkel ISROMAC conference Turbomachinery
    Matrix Viscosity and Preconditioning Techniques for Rotating Turbomachinery
    Proceedings of ISROMAC-9, 2001-FD-ABS-051
    9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Feb. 2002.
  • E. Turkel Annual Review
    Preconditioning Techniques in Computational Fluid Dynamics,
    Annual Reviews in Fluid Mechanics 1999, Vol 31, 385-416, 1999.
  • E. Turkel, V. Vatsa and V. Venkatakhrishnan Norfolk
    Uni-directional Implicit Acceleration Techniques, 14th AIAA Computational Fluid Dynamics Conference, AIAA paper 99-3265, 1999.
  • E. Turkel and C.S. Swanson VKI Lecture Notes, 1997 Central Difference Methods for Aerodynamic Problems,
  • E. Turkel cfdreview
    Review of Preconditioning for the Compressible Fluid Dynamic Equations, CFD Review, John Wiley and Sons, 1998, M. M. Hafez and K. Oshima editors.
  • E. Turkel and Radespiel VKI Lecture Notes, 1997 Preconditioning
  • D.L. Tweedt, R.V. Chima and E. Turkel Turbomachinery
    Preconditioning for Numerical Simulation of Low Mach Number Three-Dimensional Viscous Turbomachinery Flows,
    28th AIAA Fluid Dynamics Conference, AIAA paper 97-1828, 1997.
  • Turkel, Radepiel and Kroll Two Preconditioning Methods
    "Assessment of Two Preconditioning Methods for Aerodynamic Problems," \emph{Computers and Fluids} 26:613-634, 1997.
  • R.C. Swanson, R. Radespiel and E. Turkel CUSP
    On Some Numerical Dissipation Schemes,
    13th AIAA Computational Fluid Dynamics Conference,
    AIAA paper 97-1945, 1997.
  • E. Turkel Preconditioning Squared
    Preconditioning-Squared Methods for Multidimensional Aerodynamics,
    13th AIAA Computational Fluid Dynamics Conference,
    AIAA paper 97-2025, 1997.
  • P. Roe and E. Turkel Diagonalization
    The Quest for Diagonalization of Dufferential Systems,
    Barriers and Challenges in Computational Fluid Dynamics,
    Kluwer Publisher, 1997.
  • E. Turkel, V.N. Vatsa and R. Radespiel,
    Preconditioning Methods for Low Speed Flow,
    14th AIAA Applied Aerodynamics Conference, AIAA paper 96-2460, 1996.
  • S.V. Tsynkov, E. Turkel and S. Abarbanel,
    External Flow Computations Using Global Boundary Conditions,
    AIAA Journal (1996) 34:700-706.
  • E. Turkel, Fiterman and van Leer Accuracy of Solutions
    Pressure Updating Methods for Steady-State Fluid Equations,
    Proceedings 12th AIAA Computational Fluid Dynamics Conference,
    p68-76, AIAA paper 95-1652-CP, 1995.
  • B. Van Leer, L. Mesaros, C.H. Tai and E. Turkel,
    Local Preconditioning in a Stagnation Point,
    Proceedings 12th AIAA Computational Fluid Dynamics Conference,
    p88-101, AIAA paper 95-1654-CP, 1995.
  • E. Turkel, Review paper
    Review of Preconditioning Methods for Fluid Dynamics,
    Applied Numerical Mathematics, 12:257-284, 1993.
  • R.C. Swanson, E. Turkel,
    On Central Difference and Upwind Schemes,
    Journal of Computational Physics, 101: 292-306, 1992.
  • R.C. Swanson and E. Turkel,
    A Multistage Time-Stepping Scheme for the Navier-Stokes Equations,
    AIAA Aerospace Sciences Meeting, AIAA paper 85-0035, 1985.
  • A. Jameson, W. Schmidt and E. Turkel Euler equations with Runge-Kutta methods,
    Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,
    AIAA Paper 8l-l259, 198l.
  • A. Jameson and E. Turkel,
    Implicit Schemes and LU Decompositions,
    Mathematics of Computations, 37: 385-397, 198l.
  • A. Bayliss and E. Turkel,
    Radiation Boundary Conditions for Wave-Like Equation,
    Communications in Pure and Applied Mathematics, 33: 707-725, 1980.
  • D. Gottlieb, E. Turkel,
    Dissipative Two-Four Methods for Time Dependent Problems,
    Mathematics of Computations, 30: 703-723, 1976.

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