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.

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  1. Wang, Sulin; Xu, Zhengfu: Total variation bounded flux limiters for high order finite difference schemes solving one-dimensional scalar conservation laws (2019)
  2. Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.; Tomov, Vladimir Z.: High-order multi-material ALE hydrodynamics (2018)
  3. Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.: High-order upwind schemes for the wave equation on overlapping grids: Maxwell’s equations in second-order form (2018)
  4. Burton, D. E.; Morgan, N. R.; Charest, M. R. J.; Kenamond, M. A.; Fung, J.: Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme (2018)
  5. Coquel, Frédéric; Jin, Shi; Liu, Jian-Guo; Wang, Li: Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws (2018)
  6. Guermond, Jean-Luc; de Luna, Manuel Quezada; Popov, Bojan; Kees, Christopher E.; Farthing, Matthew W.: Well-balanced second-order finite element approximation of the shallow water equations with friction (2018)
  7. Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Tomas, Ignacio: Second-order invariant domain preserving approximation of the Euler equations using convex limiting (2018)
  8. Hansel, Joshua E.; Ragusa, Jean C.: Flux-corrected transport techniques applied to the radiation transport equation discretized with continuous finite elements (2018)
  9. Kovyrkina, O. A.; Ostapenko, V. V.: Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws (2018)
  10. Kuznetsov, Maxim B.; Gubernov, Vladimir V.; Kolobov, Andrey V.: Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling (2018)
  11. Kuznetsov, Maxim B.; Kolobov, Andrey V.: Transient alleviation of tumor hypoxia during first days of antiangiogenic therapy as a result of therapy-induced alterations in nutrient supply and tumor metabolism -- analysis by mathematical modeling (2018)
  12. Porter-Sobieraj, Joanna; Słodkowski, Marcin; Kikoła, Daniel; Sikorski, Jan; Aszklar, Paweł: A MUSTA-FORCE algorithm for solving partial differential equations of relativistic hydrodynamics (2018)
  13. Samalerk, Pawarisa; Pochai, Nopparat: Numerical simulation of a one-dimensional water-quality model in a stream using a Saulyev technique with quadratic interpolated initial-boundary conditions (2018)
  14. Sidilkover, David: Towards unification of the vorticity confinement and shock capturing (TVD and ENO/WENO) methods (2018)
  15. Tunik, Yu. V.: Numerical solution of test problems using a modified Godunov scheme (2018)
  16. Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard: Fully computable error estimation of a nonlinear, positivity-preserving discretization of the convection-diffusion-reaction equation (2017)
  17. Anderson, R.; Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Quezada de Luna, M.; Rieben, R.; Tomov, V.: High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation (2017)
  18. Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr: An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes (2017)
  19. Barrenechea, Gabriel R.; Knobloch, Petr: Analysis of a group finite element formulation (2017)
  20. Dubey, Ritesh Kumar; Biswas, Biswarup: An analysis on induced numerical oscillations by Lax-Friedrichs scheme (2017)

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