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. John, Volker; Knobloch, Petr; Korsmeier, Paul: On the solvability of the nonlinear problems in an algebraically stabilized finite element method for evolutionary transport-dominated equations (2021)
  2. Lochab, Ruchika; Kumar, Vivek: An improved flux limiter using fuzzy modifiers for hyperbolic conservation laws (2021)
  3. Santos, Ricardo; Alves, Leonardo: A comparative analysis of explicit, IMEX and implicit strong stability preserving Runge-Kutta schemes (2021)
  4. 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)
  5. 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)
  6. 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)
  7. Guermond, Jean-Luc; Popov, Bojan; Saavedra, Laura: Second-order invariant domain preserving ALE approximation of hyperbolic systems (2020)
  8. Kuzmin, Dmitri: Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws (2020)
  9. Kuzmin, Dmitri; Quezada de Luna, Manuel: Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws (2020)
  10. Kuznetsov, Maxim; Kolobov, Andrey: Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model (2020)
  11. Lin, Bo; Zhuang, Chijie; Cai, Zhenning; Zeng, Rong; Bao, Weizhu: An efficient and accurate MPI-based parallel simulator for streamer discharges in three dimensions (2020)
  12. Molina, Jorge; Ortiz, Pablo: A continuous finite element solution of fluid interface propagation for emergence of cavities and geysering (2020)
  13. Shokin, Yurii; Winnicki, Ireneusz; Jasinski, Janusz; Pietrek, Slawomir: High order modified differential equation of the Beam-Warming method. I. The dispersive features (2020)
  14. Shokin, Yurii; Winnicki, Ireneusz; Jasinski, Janusz; Pietrek, Slawomir: High order modified differential equation of the beam-warming method. II: The dissipative features (2020)
  15. 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)
  16. Deng, Xi; Shimizu, Yuya; Xiao, Feng: A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm (2019)
  17. Feng, Dianlei; Neuweiler, Insa; Nackenhorst, Udo; Wick, Thomas: A time-space flux-corrected transport finite element formulation for solving multi-dimensional advection-diffusion-reaction equations (2019)
  18. Guermond, Jean-Luc; Popov, Bojan; Tomas, Ignacio: Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems (2019)
  19. Lee, David; Petersen, M.; Lowrie, R.; Ringler, T.: Tracer transport within an unstructured grid Ocean model using characteristic discontinuous Galerkin advection (2019)
  20. Lohmann, Christoph: Algebraic flux correction schemes preserving the eigenvalue range of symmetric tensor fields (2019)

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