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
More filters
Journal ArticleDOI
Design principles for bounded higher-order convection schemes - a unified approach
N. P. Waterson,Herman Deconinck +1 more
TL;DR: The design of bounded, higher-order convection schemes is considered with a view to selecting those discretizations giving good resolution of sharp gradients, while at the same time providing competitive accuracy and convergence behaviour when applied to smooth, recirculating flows.
Journal ArticleDOI
Assessment of skill and portability in regional marine biogeochemical models : Role of multiple planktonic groups
Marjorie A. M. Friedrichs,Marjorie A. M. Friedrichs,Jeffrey A. Dusenberry,Laurence A. Anderson,Robert Armstrong,Fei Chai,James R. Christian,Scott C. Doney,John P. Dunne,Masahiko Fujii,Masahiko Fujii,Raleigh R. Hood,Dennis J. McGillicuddy,J. Keith Moore,Markus Schartau,Yvette H. Spitz,Jerry D. Wiggert +16 more
TL;DR: In this paper, 12 lower trophic level models of varying complexity are evaluated in two distinct regions (equatorial Pacific and Arabian Sea) and a consistent variational adjoint implementation assimilating chlorophyll-a, nitrate, export, and primary productivity was applied.
Book ChapterDOI
High Order ENO and WENO Schemes for Computational Fluid Dynamics
TL;DR: The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible.
Journal ArticleDOI
Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection
B. P. Leonard,Simin Mokhtari +1 more
TL;DR: The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high-resolution non-oscillatory multidimensional steady-state high-speed convective modelling.
Journal ArticleDOI
A low-diffusive and oscillation-free convection scheme
TL;DR: In this paper, a higher-resolution and bounded discretization scheme is proposed for calculations of incompressible steady flows with finite-volume methods, which combines a second-order upstream-weighted approximation with the first-order upwind differencing under the control of a convection boundedness criterion.
References
More filters
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.