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. Seal, David C.; Tang, Qi; Xu, Zhengfu; Christlieb, Andrew J.: An explicit high-order single-stage single-step positivity-preserving finite difference WENO method for the compressible Euler equations (2016)
  2. Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng: Simulation of all-scale atmospheric dynamics on unstructured meshes (2016)
  3. Sun, Ziyao; Inaba, Satoshi; Xiao, Feng: Boundary variation diminishing (BVD) reconstruction: a new approach to improve Godunov schemes (2016)
  4. Thorne, Jonathan; Katz, Aaron: Source term discretization effects on the steady-state accuracy of finite volume schemes (2016)
  5. Welk, Martin: Multivariate median filters and partial differential equations (2016)
  6. Xiong, Tao; Qiu, Jing-Mei; Xu, Zhengfu: Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations (2016)
  7. Yang, Pei; Xiong, Tao; Qiu, Jing-Mei; Xu, Zhengfu: High order maximum principle preserving finite volume method for convection dominated problems (2016)
  8. Zeng, Xianyi: A general approach to enhance slope limiters in MUSCL schemes on nonuniform rectilinear grids (2016)
  9. Bidadi, Shreyas; Rani, Sarma L.: On the stability and diffusive characteristics of Roe-MUSCL and Runge-Kutta schemes for inviscid Taylor-Green vortex (2015)
  10. Kouhi, Mohammad; Oñate, Eugenio: An implicit stabilized finite element method for the compressible Navier-Stokes equations using finite calculus (2015)
  11. Zakari, M.; Caquineau, H.; Hotmar, P.; Ségur, P.: An axisymmetric unstructured finite volume method applied to the numerical modeling of an atmospheric pressure gas discharge (2015)
  12. Zerroukat, M.; Allen, T.: On the monotonic and conservative transport on overset/Yin-Yang grids (2015)
  13. Zhang, Di; Jiang, Chunbo; Liang, Dongfang; Cheng, Liang: A review on TVD schemes and a refined flux-limiter for steady-state calculations (2015)
  14. Bidadi, Shreyas; Rani, Sarma L.: Quantification of numerical diffusivity due to TVD schemes in the advection equation (2014)
  15. Bigot, Barbara; Bonometti, Thomas; Lacaze, Laurent; Thual, Olivier: A simple immersed-boundary method for solid-fluid interaction in constant- and stratified-density flows (2014)
  16. Boscheri, Walter; Balsara, Dinshaw S.; Dumbser, Michael: Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers (2014)
  17. Dimarco, G.; Pareschi, L.: Numerical methods for kinetic equations (2014)
  18. Guermond, Jean-Luc; Nazarov, Murtazo: A maximum-principle preserving (C^0) finite element method for scalar conservation equations (2014)
  19. Javadi, Ali; Pasandideh-Fard, Mahmoud; Malek-Jafarian, Majid: Analysis of one-dimensional inviscid and two-dimensional viscous flows using entropy preserving method (2014)
  20. Kent, James; Jablonowski, Christiane; Whitehead, Jared P.; Rood, Richard B.: Determining the effective resolution of advection schemes. Part II: numerical testing (2014)

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