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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Advanced numerical methods and software approaches for semiconductor device simulation
TL;DR: Several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrod dynamic, and quantum hydrodynamic systems are presented.
Journal ArticleDOI
A family of ELLAM schemes for advection‐diffusion‐reaction equations and their convergence analyses
Upwind discretization of the steady Navier-Stokes equations
TL;DR: In this paper, a discretization method for the full, steady, compressible Navier-Stokes equations is presented, which makes use of quadrilateral finite volumes and consists of an upwind discretisation of the convective part and a central discretizing of the diffusive part.
Journal ArticleDOI
Elastic instability and secondary flow in cross-slot flow of wormlike micellar solutions
TL;DR: In this paper, the authors investigated the role that the breakage of worm-like micelles plays in the formation of lip vortices and the development of an asymmetric elastic instability.
Journal ArticleDOI
Combat modelling with partial differential equations
Therese Keane,Therese Keane +1 more
TL;DR: In this article, the authors extend Lanchesters ODEs, constructing a new physically meaningful system of partial differential equations for modeling the nature of conflict, including the emergence of cohesive density profiles and regrouping after suffering losses in both one and two dimensions.
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.