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 221 articles , 2 standard articles )

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  1. Kuzmin, D.; Turek, S.: Flux correction tools for finite elements (2002)
  2. Oliveira, Anabela; Fortunato, André B.: Toward an oscillation-free, mass conservative, Eulerian-Lagrangian transport model. (2002)
  3. Raines, Alla: Study of a shock wave structure in gas mixtures on the basis of the Boltzmann equation (2002)
  4. Sokolov, Igor’ V.; Timofeev, Eugene V.; Sakai, Jun-ichi; Takayama, Kazuyoshi: Artificial wind--a new framework to construct simple and efficient upwind shock-capturing schemes (2002)
  5. Wang, Z. J.: Spectral (finite) volume method for conservation laws on unstructured grids. Basic formulation (2002)
  6. Wei, G. W.: Shock capturing by anisotropic diffusion oscillation reduction (2002)
  7. Ewing, Richard E.; Wang, Hong: A summary of numerical methods for time-dependent advection-dominated partial differential equations (2001)
  8. Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline: The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids. (2001)
  9. Filbet, Francis; Sonnendrücker, Eric; Bertrand, Pierre: Conservative numerical schemes for the Vlasov equation (2001)
  10. Nutaro, T.; Riyavong, S.; Ruffolo, D.: Application of a generalized total variation diminishing algorithm to cosmic ray transport and acceleration. (2001)
  11. Sheu, Tony W. H.; Fang, C. C.: High resolution finite element analysis of shallow water equations in two dimensions (2001)
  12. Thuburn, John; Haine, Thomas W. N.: Adjoints of nonoscillatory advection schemes (2001)
  13. Xiao, Feng; Yabe, Takashi: Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation (2001)
  14. Xu, Kun: A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method (2001)
  15. Font, José A.: Numerical hydrodynamics in general relativity (2000)
  16. Ghosh, S.; Niyogi, P.: A study of non-oscillatory schemes based on LED principle for inviscid flow computation past airfoils (2000)
  17. Langseth, Jan Olav; LeVeque, Randall J.: A wave propagation method for three-dimensional hyperbolic conservation laws (2000)
  18. Lyra, P. R. M.; Morgan, K.: A review and comparative study of upwind biased schemes for compressible flow computation. II: 1-D higher-order schemes (2000)
  19. Tóth, Gábor: The (\nabla\cdotB=0) constraint in shock-capturing magnetohydrodynamics codes (2000)
  20. Kuo, Hung-Chi; Leou, Tzay-Ming; Williams, R. T.: A study on the high-order Smolarkiewicz methods (1999)

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