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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A novel multidimensional solution reconstruction and edge-based limiting procedure for unstructured cell-centered finite volumes with application to shallow water dynamics
A. I. Delis,Ioannis K. Nikolos +1 more
TL;DR: In this article, a modification to a reconstruction procedure for cell-centered finite volume (CCFV) schemes is introduced, which takes into account geometrical characteristics of computational triangular meshes.
Journal Article
A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows
van Einar Brummelen,Barry Koren +1 more
TL;DR: This work shows that pressure oscillations are induced by the loss of a pressure-invariance property under discretization, and introduces a non-oscillatory conservative method for barotropic two-fluid flows.
Journal ArticleDOI
Assessing maximum possible damage for contaminant release events
Fernando Camelli,Rainald Löhner +1 more
TL;DR: In this paper, the combined use of damage criteria, genetic algorithms and advanced CFD solvers provides an effective strategy to identify locations of releases that produce maximum damage, and the implementation is simple and does not require any change to flow solvers.
Journal ArticleDOI
A new shock-capturing technique based on Moving Least Squares for higher-order numerical schemes on unstructured grids
TL;DR: A shock detection technique based on Moving Least Squares reproducing kernel approximations that results in a very accurate detection of the shock position in multidimensional flows and is comparable to those of essentially non-oscillatory ( ENO) and weighted ENO (WENO) schemes.
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.