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.
This work was supported by the U.S. Department of Energy
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. P. Boris. A fluid transport algorithm that works. In Computing as a Language of Physics, pages 171–189. International Atomic Energy Commission, 1971.
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.
A. J. Chorin. Random choice solution of hyperbolic systems. Journal of Computational Physics, 22:517–536, 1976.
A. J. Chorin. Random choice methods with application to reacting gas flow. Journal of Computational Physics, 25:252–272, 1977.
P. Colella and P. R. Woodward. The Piecewise-Parabolic Method (PPM) for gas-dynamical simulations. Journal of Computational Physics, 54:174–201, 1984.
C. R. DeVore. An Improved Limiter for Multidimensional Flux-Corrected Transport. NRL Memorandum Report 6440-98-8330, Naval Research Laboratory, Washington, DC, 1998.
C. K. Forester. Higher order monotonic convective difference schemes. Journal of Computational Physics, 23:1–22, 1977.
J. Glimm. Solution in the large for nonlinear hyperbolic systems of equations. Communications on Pure and Applied Mathematics, 18:697–715, 1955.
H.-O. Kreiss and J. Oliger. Comparison of accurate methods for the integration of hyperbolic equations. Tellus, 24:199, 1972.
B. E. McDonald. Flux-corrected pseudospectral method for scalar hyperbolic conservation laws. Journal of Computational Physics, 82:413, 1989.
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.
P. R. Woodward and P. Colella. The numerical simulation of two-dimensional flow with strong shocks. Journal of Computational Physics, 54:115–173, 1984.
S. T. Zalesak. Fully multidimensional Flux-Corrected Transport algorithms for fluids. Journal of Computational Physics, 31:335–362, 1979.
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.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Zalesak, S.T. (2005). The Design of Flux-Corrected Transport (FCT) Algorithms For Structured Grids. In: Kuzmin, D., Löhner, R., Turek, S. (eds) Flux-Corrected Transport. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27206-2_2
Download citation
DOI: https://doi.org/10.1007/3-540-27206-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23730-3
Online ISBN: 978-3-540-27206-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)