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. Frank, Florian; Rupp, Andreas; Kuzmin, Dmitri: Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation (2020)
  2. Kuzmin, Dmitri: Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws (2020)
  3. Kuznetsov, Maxim; Kolobov, Andrey: Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model (2020)
  4. Molina, Jorge; Ortiz, Pablo: A continuous finite element solution of fluid interface propagation for emergence of cavities and geysering (2020)
  5. Guermond, Jean-Luc; Popov, Bojan; Tomas, Ignacio: Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems (2019)
  6. Lohmann, Christoph: Algebraic flux correction schemes preserving the eigenvalue range of symmetric tensor fields (2019)
  7. Wang, Sulin; Xu, Zhengfu: Total variation bounded flux limiters for high order finite difference schemes solving one-dimensional scalar conservation laws (2019)
  8. Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.; Tomov, Vladimir Z.: High-order multi-material ALE hydrodynamics (2018)
  9. 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)
  10. Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr; Rankin, Richard: A unified analysis of algebraic flux correction schemes for convection-diffusion equations (2018)
  11. 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)
  12. 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)
  13. 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)
  14. Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Tomas, Ignacio: Second-order invariant domain preserving approximation of the Euler equations using convex limiting (2018)
  15. Hansel, Joshua E.; Ragusa, Jean C.: Flux-corrected transport techniques applied to the radiation transport equation discretized with continuous finite elements (2018)
  16. Kovyrkina, O. A.; Ostapenko, V. V.: Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws (2018)
  17. Kuznetsov, Maxim B.; Gubernov, Vladimir V.; Kolobov, Andrey V.: Analysis of anticancer efficiency of combined fractionated radiotherapy and antiangiogenic therapy via mathematical modelling (2018)
  18. 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)
  19. Porter-Sobieraj, Joanna; Słodkowski, Marcin; Kikoła, Daniel; Sikorski, Jan; Aszklar, Paweł: A MUSTA-FORCE algorithm for solving partial differential equations of relativistic hydrodynamics (2018)
  20. 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)

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