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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Wavenumber-extended high-order oscillation control finite volume schemes for multi-dimensional aeroacoustic computations
TL;DR: A new numerical method toward accurate and efficient aeroacoustic computations of multi-dimensional compressible flows has been developed and the new distinguishing mechanism which is based on the Gibbs phenomenon in discontinuity is introduced to eliminate the excessive numerical dissipation in the continuous region by the restricted application of MLP.
Journal ArticleDOI
A finite volume method for numerical simulation of shallow water models with porosity
TL;DR: In this article, a finite volume method for numerical simulation of one and two dimensions of shallow water equations with porosity is presented. But the method is not suitable for the case of large porosity.
Journal ArticleDOI
Solid barriers for windblown sand mitigation: Aerodynamic behavior and conceptual design guidelines
TL;DR: In this article, the aerodynamic effects of sand barrier on the flow is analyzed and an empirical dimensionless performance estimator is proposed and used to provide general design guidelines for sand barrier.
Journal ArticleDOI
Numerical method for optimal control problems governed by nonlinear hyperbolic systems of PDEs
TL;DR: In this paper, a numerical method for the solution to linear adjoint equations arising, for example, in optimization problems governed by hyperbolic systems of nonlinear conservation and balance laws in one space dimension is developed.
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.