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. Bochev, Pavel; Ridzal, Denis; D’Elia, Marta; Perego, Mauro; Peterson, Kara: Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to algebraic flux correction (2020)
  2. 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)
  3. Galindez-Ramirez, G.; Carvalho, D. K. E.; Lyra, P. R. M.: Numerical simulation of 1-D oil and water displacements in petroleum reservoirs using the correction procedure via reconstruction (CPR) method (2020)
  4. Kuzmin, Dmitri: Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws (2020)
  5. Kuzmin, Dmitri; Quezada de Luna, Manuel: Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws (2020)
  6. Kuznetsov, Maxim; Kolobov, Andrey: Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model (2020)
  7. Molina, Jorge; Ortiz, Pablo: A continuous finite element solution of fluid interface propagation for emergence of cavities and geysering (2020)
  8. Shokin, Yurii; Winnicki, Ireneusz; Jasinski, Janusz; Pietrek, Slawomir: High order modified differential equation of the Beam-Warming method. I. The dispersive features (2020)
  9. Shokin, Yurii; Winnicki, Ireneusz; Jasinski, Janusz; Pietrek, Slawomir: High order modified differential equation of the beam-warming method, II. The dissipative features (2020)
  10. Tann, Siengdy; Deng, Xi; Loubère, Raphaël; Xiao, Feng: Solution property preserving reconstruction BVD+MOOD scheme for compressible Euler equations with source terms and detonations (2020)
  11. Guermond, Jean-Luc; Popov, Bojan; Tomas, Ignacio: Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems (2019)
  12. Lee, David; Petersen, M.; Lowrie, R.; Ringler, T.: Tracer transport within an unstructured grid Ocean model using characteristic discontinuous Galerkin advection (2019)
  13. Lohmann, Christoph: Algebraic flux correction schemes preserving the eigenvalue range of symmetric tensor fields (2019)
  14. Wang, Sulin; Xu, Zhengfu: Total variation bounded flux limiters for high order finite difference schemes solving one-dimensional scalar conservation laws (2019)
  15. Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.; Tomov, Vladimir Z.: High-order multi-material ALE hydrodynamics (2018)
  16. 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)
  17. Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr; Rankin, Richard: A unified analysis of algebraic flux correction schemes for convection-diffusion equations (2018)
  18. 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)
  19. 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)
  20. 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)

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