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
Simulation of transients in natural gas pipelines using hybrid TVD schemes
Junyang Zhou,Michael A. Adewumi +1 more
TL;DR: In this article, an explicit 5-point, second-order-accurate total variation diminishing (TVD) scheme is formulated to solve the homogeneous system of non-linear hyperbolic conservation laws.
Journal ArticleDOI
Controlling spurious diapycnal mixing in eddy-resolving height-coordinate ocean models – Insights from virtual deliberate tracer release experiments
TL;DR: In this article, a reentrant channel configuration of the MIT General Circulation Model that approximates the Antarctic Circumpolar Current is used to examine the issues of spurious diapycnal mixing in frontal flow.
Journal ArticleDOI
Non-Oscillatory Central Schemes for the Incompressible 2-D Euler Equations
Doron Levy,Eitan Tadmor +1 more
TL;DR: In this article, a non-oscillatory central scheme, first presented in the con- text of Hyperbolic conservation laws in (28), followed by (15), to the framework of the incompressible Euler equations in their vorticity formulation is adopted.
Journal ArticleDOI
Transport and Acceleration of Energetic Charged Particles near an Oblique Shock
TL;DR: In this paper, a numerical simulation code was developed to study the steady state acceleration of energetic particles at an oblique shock and explain observed precursors of Forbush decreases of Galactic cosmic rays before the arrival of an interplanetary shock induced by solar activity.
Journal ArticleDOI
Practical aspects in comparing shock-capturing schemes for dam break problems
TL;DR: In this paper, a finite-volume numerical method is developed for solving the unsteady, three-dimensional Reynolds-averaged Navier-Stokes equations, closed with the k-ω turbulence model, in generalized curvilinear coordinates and applied to study the flow in the vicinity of a typical abutment geometry with a fixed, flat bed.
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.