SHASTA

Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. This paper describes a class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built around a technique called “flux correction.” These flux-corrected transport algorithms are of indeterminate order but yield realistic, accurate results. In addition to the mass-conserving property of most conventional algorithms, the FCT algorithms strictly maintain the positivity of actual mass densities so steep gradients and inviscid shocks are handled particularly well. This first paper concentrates on a simple one-dimensional version of FCT utilizing SHASTA, a new transport algorithm for the continuity equation, which is described in detail.


References in zbMATH (referenced in 203 articles , 2 standard articles )

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  1. Tóth, Gábor: The (\nabla\cdotB=0) constraint in shock-capturing magnetohydrodynamics codes (2000)
  2. Kuo, Hung-Chi; Leou, Tzay-Ming; Williams, R. T.: A study on the high-order Smolarkiewicz methods (1999)
  3. Sheu, T. W. H.; Fang, C. C.; Tsai, S. F.: Application of an element-by-element BiCGSTAB iterative solver to a monotonic finite element model (1999)
  4. Stone, James M.: The ZEUS code for astrophysical magnetohydrodynamics: New extensions and applications (1999)
  5. van Leer, Bram: An introduction to the article “Reminiscences about difference schemes” by S. K. Godunov (1999)
  6. Chippada, S.; Dawson, C. N.; Martinez, M. L.; Wheeler, M. F.: A Godunov-type finite volume method for the system of shallow water equations (1998)
  7. Rider, William J.; Kothe, Douglas B.: Reconstructing volume tracking (1998)
  8. Sheu, Tony W. H.; Wang, S. K.; Tsai, S. F.: Development of a high-resolution scheme for a multi-dimensional advection-diffusion equation (1998)
  9. Boris, Jay P.; Book, David L.: Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works (1997)
  10. Chen, Gui-Qiang; Liu, Jian-Guo: Convergence of difference schemes with high resolution for conservation laws (1997)
  11. Hirsch, Ch.: Introduction to “Towards the ultimate conservative difference scheme. V: A second-order sequel to Godunov’s method” (1997)
  12. Margolin, L. G.: Introduction to “An arbitrary Lagrangian-Eulerian computing method for all flow speeds” (1997)
  13. Sakai, Katsuhiro; Zhang, Gen Sheng: A numerical scheme for transport equations with spatially distributed coefficients based on locally exact difference method (1997)
  14. Tai, C. H.; Chiang, D. C.; Su, Y. P.: Explicit time marching methods for the time-dependent Euler computations (1997)
  15. Zalesak, Steven T.: Introduction to “Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works” (1997)
  16. Noelle, Sebastian: Convergence of higer order finite volume schemes on irregular grids (1995)
  17. Davis, Stephen F.: Flux difference splittings and limiters for the resolution of contact discontinuities (1994)
  18. Ton, V. T.; Karagozian, A. R.; Marble, F. E.; Osher, S. J.; Engquist, B. E.: Numerical simulations of high-speed chemically reacting flow (1994)
  19. Jameson, Antony: Computational algorithms for aerodynamic analysis and design (1993)
  20. Tyndall, M. B.: Numerical modelling of shocks in solids with elastic-plastic conditions (1993)

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