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 rationale for implicit turbulence modelling
Len G. Margolin,William J. Rider +1 more
TL;DR: In this paper, the authors present a rationale for the success of nonoscillatory finite volume difference schemes in modeling turbulent flows without need of subgrid scale models, and demonstrate that these truncation terms have physical justification, representing the modifications to the governing equations that arise when one considers the motion of finite volumes of fluid over finite intervals of time.
Journal ArticleDOI
A three-dimensional Eulerian model for transport and deposition of volcanic ashes
TL;DR: In this paper, an Eulerian model, named FALL3D, was developed for the transport and deposition of volcanic ashes based on the advection-diffusion-sedimentation equation with a turbulent diffusion given by the gradient transport theory.
Journal ArticleDOI
Large Eddy simulation of a turbulent non-premixed flame
N. Branley,W.P. Jones +1 more
TL;DR: In this paper, a large eddy simulation (LES) was applied to the calculation of a turbulent hydrogen diffusion flame using a conserved scalar formalism, and the results of the simulations show that LES is capable of producing good agreement with measurements of mean velocity, Reynolds stresses and fluxes.
Journal ArticleDOI
Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws
Joseph E. Flaherty,R. M. Loy,Mark S. Shephard,Boleslaw K. Szymanski,James D. Teresco,Louis H. Ziantz +5 more
TL;DR: To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size and processor load imbalances are corrected by using traversals of an octree representing a spatial decomposition of the domain.
Journal ArticleDOI
Robust numerical methods for PDE models of Asian options
TL;DR: It is demonstrated that numerical PDE techniques commonly used in nance for standard options are inaccurate in the case of Asian options and modi cations which alleviate this problem are illustrated.
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.