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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SEMI‐IMPLICIT FINITE VOLUME SHALLOW‐WATER FLOW AND SOLUTE TRANSPORT SOLVER WITH k–ε TURBULENCE MODEL
TL;DR: In this paper, a semi-implicit finite volume scheme for shallow water flow with the hydrostatic pressure assumption has been developed using the σ-coordinate system, incorporating a standard κ-e turbulence transport model and variable density solute transport with the Boussinesq approximation for the resulting horizontal pressure gradients.
Journal ArticleDOI
An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics
TL;DR: A novel upwind vertex centred finite volume algorithm with three key novelties is introduced to extend the range of applications towards the incompressibility limit and demonstrates hyperbolicity and the correct time step bounds for non-isothermal processes.
Journal ArticleDOI
A high-resolution finite-difference scheme for nonuniform grids
TL;DR: In this paper, a higher-order, high-resolution finite-difference scheme for non-uniform grids is presented, derived rigorously from Taylor series expansion at nonuniform grid points with a total-variation-diminishing constraint applied.
Journal ArticleDOI
Assessment of very high order of accuracy in implicit LES models
TL;DR: This paper looks at the use of high-resolution and very high-order methods for implicit large-eddy simulation (ILES), with the specific example of simulating the multicomponent two-dimensional single-mode Richtmyer-Meshkov instability, indicating that the ILES approach is capable of providing accurately physical information despite the lack of any formal subgrid model.
Journal ArticleDOI
A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part II. Nonlinear oscillations
TL;DR: In this paper, a simplified quasi-one-dimensional model of thermoacoustic devices formulated in Part I [Watanabe et al., J. Acoust. Soc. 102, 3484, 3496 (1997)] is studied in the nonlinear regime.
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.