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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Numerical methods for reactive transport on rectangular and streamline-oriented grids
TL;DR: In this article, two cell-centered finite volume schemes are presented for the simulation of advection-dominated reactive transport in groundwater, one based on rectangular grids and the other based on streamline-oriented grids.
Journal ArticleDOI
A robust high‐resolution finite volume scheme for the simulation of long waves over complex domains
TL;DR: In this paper, the propagation, runup and rundown of long surface waves are numerically investigated, initially in one dimension, using a well-balanced high-resolution finite volume scheme.
Journal ArticleDOI
Anisotropic mesh adaptivity for multi-scale ocean modelling.
TL;DR: An optimization-based approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics and Comparisons are made between the results obtained with uniform isotropic resolution, isotropics adaptive resolution and fully an isotropic adaptive resolution.
Journal Article
Method of lines and direct discretization: a comparison for linear advection
TL;DR: Two related schemes are compared for two-dimensional linear advection: a scheme based on dimension splitting starting from a fully discrete one-dimensional discretization, and a schemebased on the method of lines, to compare the accuracy and computational efficiency.
Journal ArticleDOI
A MUSCL method satisfying all the numerical entropy inequalities
TL;DR: A method to determine a slope reconstruction satisfying all the exact numerical entropy inequalities is given, which avoids inhomogeneous slope limitations and gives a convergence rate of Δx l/2.
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.