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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Numerical study of coastal sandbar migration, by hydro-morphodynamical coupling
TL;DR: In this paper, a finite element model based on the Legendre polynomials and on the Extended Boussinesq model was proposed to simulate the migration of real sandbars observed at Rousty beach (Mediterranean French coast).
Journal ArticleDOI
Drag on random assemblies of spheres in shear-thinning and thixotropic liquids
TL;DR: In this paper, the flow and resulting drag force in suspensions consisting of monodisperse, solid spheres, and non-Newtonian liquids have been studied via direct numerical simulations, and the results show that the shear-thinning character of the liquid manifests itself more pronounced at higher solids volume fractions.
Journal ArticleDOI
An Eulerian---Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs
TL;DR: A hybrid method is developed, which utilizes advantages of both the Eulerian finite-volume central-upwind scheme and the Lagrangian discrete characteristics method for solving the adjoint transport equation for hyperbolic balance laws in one and two space dimensions.
Journal ArticleDOI
Numerical Simulation of the Liquid Flow Into a Porous Medium with Phase Change: Application to Metal Matrix Composites Processing
C. Del Borrello,Eric Lacoste +1 more
TL;DR: In this article, a finite-volume model was developed to simulate the injection of a pure metal through a fibrous preform placed between two plane walls of a metal mold, based on the simultaneous resolutions of the heat equation, Darcy's law, and an advection equation to follow the evolution of the metal front geometry during the infiltration.
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.