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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Journal ArticleDOI
Direct Simulations of Mixing of Liquids with Density and Viscosity Differences
TL;DR: In this paper, a simulation of flow and scalar transport in stirred tanks operated in transitional and mildly turbulent regimes (Re = 3000 − 12000) is presented, where the density difference is characterized by a Richardson number (Ri) that varies in the range of 0 − 0.5.
Journal ArticleDOI
Note on the von Neumann stability of explicit one-dimensional advection schemes
TL;DR: In this article, it was shown that if explicit schemes are formulated in a consistent flux-based conservative finite-volume form, von Neumann stability analysis does not place any restriction on the allowable Courant number.
Journal ArticleDOI
Flux difference splitting for the Euler equations in one spatial co‐ordinate with area variation
TL;DR: In this paper, a schema de resolution approchee de Riemann for the equations d'Euler de la dynamique des gaz avec une coordonnee d'espace is presented.
Journal ArticleDOI
Models and methods for two-layer shallow water flows
TL;DR: By considering weak compressibility of the phases, a strictly hyperbolic formulation with pressure relaxation is obtained, which is shown to tend to the conventional two-layer model in the stiff pressure relaxation limit.
Journal ArticleDOI
A composite medium approximation for unsaturated flow in layered sediments.
TL;DR: The COMA model was implemented in a multi-phase flow simulator and tested by comparison with high-resolution simulations in which all layering heterogeneity is resolved explicitly, providing a practical method for simulating field-scale flow and transport in layered media.
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.