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
Goal-oriented a posteriori error estimates for transport problems
Dmitri Kuzmin,Sergey Korotov +1 more
TL;DR: A node-based approach to localization of global errors in the quantities of interest is pursued and a possible violation of Galerkin orthogonality is taken into account.
Journal ArticleDOI
Second-Order Upwinding through a Characteristic Time-Step Matrix for Compressible Flow Calculations
Ying Huang,Alain Lerat +1 more
TL;DR: An efficient multidimensional scheme for solving the compressible Euler equations was deduced from a centered scheme of the Lax?Wendroff type by using a special time step in the numerical flux, namely a matricial characteristic time-step.
Dissertation
Miscible flow through porous media
TL;DR: In this article, the Peaceman model is used to model viscous fluid flow through porous media, with the intended application being the displacement of oil from a reservoir by a solvent with which the oil is miscible.
Journal ArticleDOI
Coupling of hydrodynamical transport and ecological models for 2D horizontal flow
TL;DR: In this article, a combined hydrodynamical transport and ecological model system with 12 state variables is presented, and the effect of using different advection schemes on the ecological simulations is discussed.
Journal ArticleDOI
Investigation of Several Interpolation Functions for Unstructured Meshes in Conjunction with Compositional Reservoir Simulation
TL;DR: In this article, the authors present an investigation of several interpolation functions in conjunction with the element based finite-volume method (EbFVM) using unstructured triangular meshes.
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.