Journal ArticleDOI
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
TLDR
The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is described in this article.Abstract:
The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is expl...read more
Citations
More filters
Journal ArticleDOI
Well-balanced schemes for the shallow water equations with Coriolis forces
Alina Chertock,Michael Dudzinski,Alexander Kurganov,Alexander Kurganov,Maria Lukacova-Medvidova +4 more
TL;DR: This paper implements a newly developed second-order reconstruction in the context of well-balanced central-upwind and finite-volume evolution Galerkin schemes and demonstrates that the resulting finite- volume methods preserve exactly the so-called jets in the rotational frame.
Journal ArticleDOI
A second-order accurate, component-wise TVD scheme for nonlinear, hyperbolic conservation laws
Heng Yu,Yu-Ping Liu +1 more
TL;DR: A two-step, component-wise TVD scheme for nonlinear, hyperbolic conservation laws, which is obtained by combining the schemes of Mac Cormack and Warming-Beam and is found to be two times faster in computation than the usual TVD schemes based on field-by-field decomposition limiting.
Journal ArticleDOI
Modeling of residence time in the East Scott Creek Estuary, South Carolina, USA
TL;DR: In this paper, a coupled hydrodynamic and solute transport model was developed to compute average residence time in a tide-dominated East Scott Creek Estuary, South Carolina, using a tracer placed at the head of the estuary.
Journal ArticleDOI
Slope limiting for vectors: A novel vector limiting algorithm
Gabi Luttwak,Joseph Falcovitz +1 more
TL;DR: In this article, a new frame-invariant VIP monotonicity criterion for vectors is proposed to improve symmetry preservation in a number of test problems, including the Saltzman test, 2D and 3D Sedov-Taylor problems, and 2D Noh problem.
Journal ArticleDOI
The HLLC Riemann solver
TL;DR: The HLLC scheme is reviewed, starting from some historical notes, going on to a description of the algorithm as applied to some typical hyperbolic systems, and ending with an overview of some of the most significant developments and applications in the last 25 years.
References
More filters
Journal ArticleDOI
Fully multidimensional flux-corrected transport algorithms for fluids
TL;DR: In this paper, the critical flux limiting stage is implemented in multidimensions without resort to time splitting, which allows the use of flux-corrected transport (FCT) techniques in multi-dimensional fluid problems for which time splitting would produce unacceptable numerical results.
Journal ArticleDOI
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
Gary A. Sod,Gary A. Sod +1 more
TL;DR: In this paper, the finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, and Glimm's method, a random choice method, are discussed.
Journal ArticleDOI
Systems of conservation laws
Peter D. Lax,Burton Wendroff +1 more
TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.
Journal ArticleDOI
Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme
TL;DR: Fromm's second-order scheme for integrating the linear convection equation is made monotonic through the inclusion of nonlinear feedback terms in this paper, where care is taken to keep the scheme in conservation form.
Journal ArticleDOI
Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works
Jay P. Boris,David L. Book +1 more
TL;DR: A class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built around a technique called “flux correction,” which yield realistic, accurate results.