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 Viscosity in Spectral Multidomain Penalty Method-Based Simulations of Localized Turbulence
TL;DR: In this paper, a spectral multidomain method for the simulation of high Reynolds number turbulence in doubly periodic domains is investigated, and the dissipative eects of these stabilizers are quantified in terms of the numerical viscosity, using a generalization of the method previously employed to analyze numerical codes for simulation of homogeneous, isotropic turbulence in triply periodic domains.
Book ChapterDOI
Method of Lines within the Simulation Environment DIVA for Chemical Processes
R. Köhler,K. D. Mohl,Henning Schramm,Michael Zeitz,Achim Kienle,Michael Mangold,E. Stein,E. D. Gilles +7 more
Journal ArticleDOI
Comparison of numerical schemes for the solution of the advective age equation in ice sheets
TL;DR: In this article, a general difference equation is constructed from which a hierarchy of solutions for numerical age computations in ice-sheet models are derived, including first-, second-and third-order (QUICK) upstreaming as well as modi- fied TVD Lax^Friedrichs schemes (TVDLFs).
Journal ArticleDOI
On wavewise entropy inequalities for high-resolution schemes. I: the semidiscrete case
TL;DR: A new approach is developed, the method of wavewise entropy inequalities for the numerical analysis of hyperbolic conservation laws, based on a new extremum tracking theory and Vol'pert's theory of BV solutions, which yields a sharp convergence criterion.
Journal ArticleDOI
Towards an efficient numerical treatment of the transport problems in the resin transfer molding simulation
TL;DR: Chinesta et al. as mentioned in this paper proposed a fixed mesh numerical method for modeling the flow in liquid composites molding processes using a volume-of-fluid technique, and the numerical results in two dimensions are presented in order to validate the proposed numerical strategy.
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.