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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The constrained interpolation profile method for multiphase analysis
TL;DR: This work provides a comprehensive review of the strategy of the CIP method, which has a compact support and subcell resolution, including a front-capturing algorithm with functional transformation, a pressure-based algorithm, and other miscellaneous physics such as the elastic–plastic effect and surface tension.
Journal ArticleDOI
High resolution NVD differencing scheme for arbitrarily unstructured meshes
TL;DR: In this paper, a new bounded version of central differencing constructed on the compact computational molecule is proposed and its performance is compared with other popular differenced schemes on several model problems.
Journal ArticleDOI
Wave Propagation Algorithms for Multidimensional Hyperbolic Systems
TL;DR: A class of high resolution multidimensional wave-propagation algorithms is described for general time-dependent hyperbolic systems based on solving Riemann problems and applying limiter functions to the resulting waves, which are then propagated in a multiddimensional manner.
Journal ArticleDOI
SELFE: A semi-implicit Eulerian–Lagrangian finite-element model for cross-scale ocean circulation
TL;DR: This paper introduces SELFE as an open-source code available for community use and enhancement, a new finite-element model for cross-scale ocean modeling that retains key benefits of existing semi-implicit Eulerian–Lagrangian finite-volume models, but relaxation on grids, uses higher-order shape functions for elevation, and enables superior flexibility in representing the bathymetry.
Journal ArticleDOI
Characteristics of the ocean simulations in the Max Planck Institute Ocean Model (MPIOM) the ocean component of the MPI-Earth system model
Johann H. Jungclaus,Nils Fischer,Helmuth Haak,Katja Lohmann,Jochem Marotzke,Daniela Matei,Uwe Mikolajewicz,Dirk Notz,J.-S. von Storch +8 more
TL;DR: In this paper, the performance of the ocean/sea-ice model MPIOM, coupled to a new version of the atmosphere model ECHAM6 and modules for land surface and ocean biogeochemistry, is assessed for two model versions with different grid resolution in the ocean.
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.