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
An ELLAM-MFEM Solution Technique for Compressible Fluid Flows in Porous Media with Point Sources and Sinks
TL;DR: In this paper, an Eulerian?Lagrangian localized adjoint method (ELLAM) is presented to solve the transport equation for concentration. And the ELLAM-MFEM solution procedure is used to simultaneously solve the pressure equation as a system of first-order partial differential equations for the pressure and mass flow rate.
Journal ArticleDOI
Time accurate local time stepping for the unsteady shallow water equations
A. J. Crossley,Nigel Wright +1 more
TL;DR: In this article, two time accurate local time stepping (LTS) strategies originally developed for the Euler equations are presented and applied to the unsteady shallow water equations of open channel flow, allowing individual cells to be advanced to different points in time, in a time accurate fashion.
Journal ArticleDOI
A high-resolution pressure-based method for compressible flows
José Rincón,Robin L. Elder +1 more
TL;DR: In this paper, a pressure-based procedure able to model all Mach number flows is presented, which uses curvilinear coordinates and a composite low-high-order treatment with the normalized variable diagram as limiter for the convective terms.
Journal ArticleDOI
On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media
TL;DR: The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.
Journal ArticleDOI
A New Lagrangian Method for Steady Supersonic Flow Computation. Part II. Slip-line Resolution
Wai How Hui,C. Y. Loh +1 more
TL;DR: In this paper, the first-order Godunov scheme based on the new Lagrangian formulation of Hui and Van Roessel for steady supersonic flow always resolves an isolated slip-line discontinuity crisply, provided it is initially aligned with a grid line.
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.