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. Banks, J. W.; Buckner, B. Brett; Hagstrom, T.; Juhnke, K.: Discontinuous Galerkin Galerkin differences for the wave equation in second-order form (2021)
  2. De Vuyst, Florian; Fochesato, Christophe; Mahy, Vincent; Motte, Renaud; Peybernes, Mathieu: A geometrically accurate low-diffusive conservative interface capturing method suitable for multimaterial flows (2021)
  3. Guermond, Jean-Luc; Maier, Matthias; Popov, Bojan; Tomas, Ignacio: Second-order invariant domain preserving approximation of the compressible Navier-Stokes equations (2021)
  4. Hajduk, Hennes: Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws (2021)
  5. 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)
  6. Kuzmin, Dmitri: A new perspective on flux and slope limiting in discontinuous Galerkin methods for hyperbolic conservation laws (2021)
  7. Lochab, Ruchika; Kumar, Vivek: An improved flux limiter using fuzzy modifiers for hyperbolic conservation laws (2021)
  8. Nogueira Sondermann, Carina; Viggiano, Raphael; de Freitas Rachid, Felipe Bastos; Bodstein, Gustavo C. R.: A suitability analysis of transient one-dimensional two-fluid numerical models for simulating two-phase gas-liquid flows based on benchmark problems (2021)
  9. Santos, Ricardo; Alves, Leonardo: A comparative analysis of explicit, IMEX and implicit strong stability preserving Runge-Kutta schemes (2021)
  10. 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)
  11. Chung, Joseph D.; Zhang, Xiao; Kaplan, Carolyn R.; Oran, Elaine S.: The barely implicit correction algorithm for low-Mach-number flows. II: Application to reactive flows (2020)
  12. Dubey, Ritesh Kumar; Gupta, Vikas: A mesh refinement algorithm for singularly perturbed boundary and interior layer problems (2020)
  13. 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)
  14. 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)
  15. Guermond, Jean-Luc; Popov, Bojan; Saavedra, Laura: Second-order invariant domain preserving ALE approximation of hyperbolic systems (2020)
  16. Kucharik, Milan; Loubère, Raphaël: High-accurate and robust conservative remapping combining polynomial and hyperbolic tangent reconstructions (2020)
  17. Kuzmin, Dmitri: Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws (2020)
  18. Kuzmin, Dmitri; Quezada de Luna, Manuel: Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws (2020)
  19. Kuznetsov, Maxim; Kolobov, Andrey: Investigation of solid tumor progression with account of proliferation/migration dichotomy via Darwinian mathematical model (2020)
  20. 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)

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