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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Book ChapterDOI
TVD Schemes to Compute Compressible Viscous Flows on Unstructured Meshes
Philippe Rostand,Bruno Stoufflet +1 more
TL;DR: In this article, the Euler equations were extended to the Navier-Stokes system and the numerical diffusion introduced in the approximation of the convective part was chosen through a total variation analysis taking in account the physical diffusion.
Book ChapterDOI
Computational Challenges for Simulating Strongly Elastic Flows in Biology
Robert D. Guy,Becca Thomases +1 more
TL;DR: The immersed boundary method is used to simulate an undulatory swimmer in a viscoelastic fluid using a data-based model for the prescribed shape and focuses on implicit-time methods because the large elastic stresses in complex fluids necessitate high spatial resolution and long time simulations.
Journal ArticleDOI
Second-order schemes for conservation laws with discontinuous flux modelling clarifier–thickener units
TL;DR: It is proved that the FTVD scheme converges to a BVt solution of the conservation law with discontinuous flux, and the accuracy of both schemes is superior to that of the monotone first-order scheme based on the adaptation of the Engquist–Osher scheme.
Journal ArticleDOI
Higher-resolution convection schemes for flow in porous media on highly distorted unstructured grids
Sadok Lamine,Michael G. Edwards +1 more
TL;DR: In this article, a sequence of non-uniform and distorted grid formulations are developed and compared for a range of unstructured meshes with variable grid spacing, orientation and permeability.
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.