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
A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
TL;DR: Numerical results demonstrate high accuracy, stability, and robustness of the proposed second-order central-upwind scheme, which is applied to a number of two-dimensional problems including the most commonly used Keller–Segel chemotaxis model and its modern extensions.
Journal ArticleDOI
Two‐dimensional dam break flow simulation
P. Brufau,Pilar García-Navarro +1 more
TL;DR: In this article, a cell centred finite volume method based on Roe's approximate Riemann solver across the edges of the cells is presented and the results are compared for first-and second-order accuracy.
Journal ArticleDOI
High resolution methods for multidimensional advection diffusion problems in free-surface hydrodynamics
Vincenzo Casulli,Paola Zanolli +1 more
TL;DR: In this paper, the numerical solution of advection-diffusion problems in free-surface hydrodynamic is analyzed and a new finite volume scheme for unstructured grid is derived.
Journal ArticleDOI
High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter
Dmitri Kuzmin,Stefan Turek +1 more
TL;DR: A new approach to the derivation of local extremum diminishing finite element schemes is presented, which can be readily incorporated into existing flow solvers as a 'black-box' postprocessing tool for the matrix assembly routine.
Journal ArticleDOI
Accurate monotone cubic interpolation
TL;DR: In this article, the authors relax the monotonicity constraint in a geometric framework in which the median function plays a crucial role, and present algorithms for piecewise cubic interpolants, which preserve monoticity as well as uniform third and fourth-order accuracy.
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.