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. Kuznetsov, Maxim B.; Kolobov, Andrey V.: Mathematical modelling of chemotherapy combined with bevacizumab (2017)
  2. Larreteguy, Axel E.; Barceló, Luis F.; Caron, Pablo A.: A bounded upwind-downwind semi-discrete scheme for finite volume methods for phase separation problems (2017)
  3. Lohmann, Christoph: Flux-corrected transport algorithms preserving the eigenvalue range of symmetric tensor quantities (2017)
  4. Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso: Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements (2017)
  5. May, Sandra; Berger, Marsha: An explicit implicit scheme for cut cells in embedded boundary meshes (2017)
  6. Moe, Scott A.; Rossmanith, James A.; Seal, David C.: Positivity-preserving discontinuous Galerkin methods with Lax-Wendroff time discretizations (2017)
  7. Nazarov, Murtazo; Larcher, Aurélien: Numerical investigation of a viscous regularization of the Euler equations by entropy viscosity (2017)
  8. Perrotta, Andrea; Favini, Bernardo: A second-order finite-volume scheme for Euler equations: kinetic energy preserving and staggering effects (2017)
  9. Subbareddy, Pramod K.; Kartha, Anand; Candler, Graham V.: Scalar conservation and boundedness in simulations of compressible flow (2017)
  10. Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi: A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations (2016)
  11. Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing: Third-order symplectic integration method with inverse time dispersion transform for long-term simulation (2016)
  12. Guermond, Jean-Luc; Popov, Bojan: Error estimates of a first-order Lagrange finite element technique for nonlinear scalar conservation equations (2016)
  13. Hu, Lili; Li, Yao; Liu, Yingjie: A limiting strategy for the back and forth error compensation and correction method for solving advection equations (2016)
  14. Lee, D.; Lowrie, R.; Petersen, M.; Ringler, T.; Hecht, M.: A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes (2016)
  15. Lohmann, Christoph; Kuzmin, Dmitri: Synchronized flux limiting for gas dynamics variables (2016)
  16. 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)
  17. Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng: Simulation of all-scale atmospheric dynamics on unstructured meshes (2016)
  18. Sun, Ziyao; Inaba, Satoshi; Xiao, Feng: Boundary variation diminishing (BVD) reconstruction: a new approach to improve Godunov schemes (2016)
  19. Thorne, Jonathan; Katz, Aaron: Source term discretization effects on the steady-state accuracy of finite volume schemes (2016)
  20. Welk, Martin: Multivariate median filters and partial differential equations (2016)

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