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
Simple High-Order Bounded Convection Scheme to Model Discontinuities
Chung-Hsiung Lin,Chao-An Lin +1 more
TL;DR: In this article, a high-order-accurate convection scheme that satisfies the total variation diminishing (TVD) principle and is based on nonlinear functional relations between normalized variables is presented.
Journal ArticleDOI
TVD schemes for the calculation of flow in pipes of variable cross-section
José M. Corberán,M. Ll. Gascón +1 more
TL;DR: In this article, first and second order explicit TVD finite difference schemes have been adapted to the calculation of the unsteady one-dimensional flow in ducts of varying cross-sectional area.
Journal ArticleDOI
Design of an unconditionally stable, positive scheme for the K-ϵ and two-layer turbulence models
T. Jongen,Y.P. Marx +1 more
TL;DR: In this paper, an efficient and robust numerical method for the simulation of incompressible turbulent flows using turbulence modeling is presented, where the positivity of the mean turbulent kinetic energy k and of the dissipation rate ϵ is guaranteed via TVD-type constraints on the convection scheme.
Journal ArticleDOI
Higher-order multi-dimensional limiting strategy for discontinuous Galerkin methods in compressible inviscid and viscous flows
Jin Seok Park,Chongam Kim +1 more
TL;DR: Through extensive numerical analyses and computations on unstructured grids, it is demonstrated that the proposed hierarchical DG-MLP method yields outstanding performance in resolving non-compressive as well as compressive flow features.
Journal ArticleDOI
A fluid-mixture type algorithm for barotropic two-fluid flow problems
TL;DR: A simple interface-capturing approach for barotropic two-fluid flow problems in more than one space dimension using the compressible Euler equations in isentropic form as a model system with the thermodynamic property of each fluid component characterized by the Tait equation of state.
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.