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The Design of Flux-Corrected Transport (FCT) Algorithms For Structured Grids

  • Steven T. Zalesak
Part of the Scientific Computation book series (SCIENTCOMP)

Summary

A given flux-corrected transport (FCT) algorithm consists of three components: 1) a high order algorithm to which it reduces in smooth parts of the flow; 2) a low order algorithm to which it reduces in parts of the flow devoid of smoothness; and 3) a flux limiter which calculates the weights assigned to the high and low order fluxes in various regions of the flow field. One way of optimizing an FCT algorithm is to optimize each of these three components individually. We present some of the ideas that have been developed over the past 30 years toward this end. These include the use of very high order spatial operators in the design of the high order fluxes, non-clipping flux limiters, the appropriate choice of constraint variables in the critical flux-limiting step, and the implementation of a “failsafe” flux-limiting strategy.

This chapter confines itself to the design of FCT algorithms for structured grids, using a finite volume formalism, for this is the area with which the present author is most familiar. The reader will find excellent material on the design of FCT algorithms for unstructured grids, using both finite volume and finite element formalisms, in the chapters by Professors Löhner, Baum, Kuzmin, Turek, and Möller in the present volume.

Keywords

Grid Point Courant Number Density Contour Shock Tube Problem Directional Splitting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. P. Boris. A fluid transport algorithm that works. In Computing as a Language of Physics, pages 171–189. International Atomic Energy Commission, 1971.Google Scholar
  2. 2.
    J. P. Boris and D. L. Book. Flux-Corrected Transport I: SHASTA, a fluid-transport algorithm that works. Journal of Computational Physics, 11:38–69, 1973.CrossRefADSGoogle Scholar
  3. 3.
    A. J. Chorin. Random choice solution of hyperbolic systems. Journal of Computational Physics, 22:517–536, 1976.CrossRefzbMATHMathSciNetADSGoogle Scholar
  4. 4.
    A. J. Chorin. Random choice methods with application to reacting gas flow. Journal of Computational Physics, 25:252–272, 1977.CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    P. Colella and P. R. Woodward. The Piecewise-Parabolic Method (PPM) for gas-dynamical simulations. Journal of Computational Physics, 54:174–201, 1984.CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. 6.
    C. R. DeVore. An Improved Limiter for Multidimensional Flux-Corrected Transport. NRL Memorandum Report 6440-98-8330, Naval Research Laboratory, Washington, DC, 1998.Google Scholar
  7. 7.
    C. K. Forester. Higher order monotonic convective difference schemes. Journal of Computational Physics, 23:1–22, 1977.CrossRefADSzbMATHMathSciNetGoogle Scholar
  8. 8.
    J. Glimm. Solution in the large for nonlinear hyperbolic systems of equations. Communications on Pure and Applied Mathematics, 18:697–715, 1955.MathSciNetCrossRefGoogle Scholar
  9. 9.
    H.-O. Kreiss and J. Oliger. Comparison of accurate methods for the integration of hyperbolic equations. Tellus, 24:199, 1972.ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    B. E. McDonald. Flux-corrected pseudospectral method for scalar hyperbolic conservation laws. Journal of Computational Physics, 82:413, 1989.CrossRefADSzbMATHMathSciNetGoogle Scholar
  11. 11.
    G. A. Sod. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. Journal of Computational Physics, 27:1–31, 1978.CrossRefADSzbMATHMathSciNetGoogle Scholar
  12. 12.
    P. R. Woodward and P. Colella. The numerical simulation of two-dimensional flow with strong shocks. Journal of Computational Physics, 54:115–173, 1984.CrossRefADSMathSciNetzbMATHGoogle Scholar
  13. 13.
    S. T. Zalesak. Fully multidimensional Flux-Corrected Transport algorithms for fluids. Journal of Computational Physics, 31:335–362, 1979.CrossRefADSzbMATHMathSciNetGoogle Scholar
  14. 14.
    S. T. Zalesak. Very high order and pseudospectral Flux-Corrected Transport (FCT) algorithms for conservation laws. In R. Vichnevetsky and R. S. Stepleman, editors, Advances in computer methods for partial differential equations IV, pages 126–134, Rutgers University, 1981. IMACS.Google Scholar
  15. 15.
    S. T. Zalesak. A preliminary comparison of modern shock-capturing schemes: Linear advection. In R. Vichnevetsky and R. S. Stepleman, editors, Advances in computer methods for partial differential equations VI, pages 15–22, Rutgers University, 1987. IMACS.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Steven T. Zalesak
    • 1
  1. 1.Naval Research LaboratoryPlasma Physics DivisionWashington, D.C.USA

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