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
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Fast and accurate discrete ordinates methods for multidimensional radiative transfer. Part I, basic methods
TL;DR: The Newton–Krylov methods are shown to provide a natural way to incorporate the effects of nonlinearity as well as strong coupling in a way that avoids operator splitting, and the resultant method has excellent convergence properties.
Journal ArticleDOI
Divergence Form for Bed Slope Source Term in Shallow Water Equations
TL;DR: In this article, a novel technique is presented for the treatment of the bed slope source terms within the numerical solution of the shallow water equations, which consists of writing the source term as the divergence of a proper matrix, related to the static force due to bottom slope.
Journal ArticleDOI
A large Time Step Generalization of Godunov’s Method for Systems of Conservation Laws
TL;DR: In this article, a generalization of the Godunov-based method for solving conservation laws is proposed, which can be applied for arbitrarily large time steps and is easy to implement and may also be useful in other contexts, such as mesh refinement or shock tracking.
Journal ArticleDOI
Parallel adaptive hp -refinement techniques for conservation laws
TL;DR: An adaptive hp-refinement local finite element procedure for the parallel solution of hyperbolic systems of conservation laws on rectangular domains and a solution limiting procedure produces monotonic solutions near discontinuities while maintaining high-order accuracy near smooth extrema is described.
Journal ArticleDOI
A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations
TL;DR: A well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography is constructed.
References
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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.