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 Three-Dimensional, Adaptive, Godunov-Type Model for Global Atmospheric Flows
TL;DR: A Godunov-type methodology is applied to three-dimensional global atmospheric modeling, which provides the framework within which an adaptive mesh refinement (AMR) algorithm is applied, to enhance the efficiency and accuracy with which results are obtained.
Journal ArticleDOI
Computing Flows on General Three-Dimensional Nonsmooth Staggered Grids
TL;DR: In this paper, the authors generalized the Stokes equations from Cartesian grids to general boundary-fitted structured grids in three dimensions, and the resulting discretization is coordinate-invariant.
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A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows
TL;DR: The parametrized MPP flux limiter is applied only to the final stage of any explicit RK method, and the MPP property is guaranteed, while designed high order of spatial and temporal accuracy for the incompressible flow computation is not affected via extensive numerical experiments.
Journal ArticleDOI
Asymptotics, structure, and integration of sound-proof atmospheric flow equations
TL;DR: In this article, an anelastic model is obtained by suppressing @t in the mass continuity equation and slightly modifying the gravity term, whereas the pseudo-incompressible model results from dropping @tp from the pressure equation.
Journal ArticleDOI
Nonequilibrium entropy limiters in lattice Boltzmann methods
TL;DR: In this article, a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM) is presented, which can erase spurious oscillations without blurring of shocks, and do not affect smooth solutions.
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.