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 meshless generalized finite difference method for solving shallow water equations with the flux limiter technique
TL;DR: In this article, a meshless stable numerical solver is proposed to solve the non-conservative form of shallow water equations, where discontinuous solutions are allowed to transmit during the simulation, and the upwinding spatial derivatives can be approximated at every node using the half-disk shape of the star and generalized finite difference method.
Journal ArticleDOI
Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds
TL;DR: In this paper, an explicit Godunov-type solution algorithm called SEA (simple efficient algorithm) has been introduced for the shallow water equations, which is based on finite volume conservative discretisation method.
Journal ArticleDOI
Numerical simulation of multiphase flows using an enhanced Volume-of-Fluid (VOF) method
TL;DR: In this article , an improved version of the Volume-of-Fluid method (VOF-R) is introduced and utilized for modeling multiphase/multifluid flows and transport processes.
Journal ArticleDOI
On a practical implementation of particle methods
TL;DR: In this article, a practical implementation of deterministic particle methods for solving transport equations with discontinuous coefficients and/or initial data, and related problems is devoted to practical implementation, where the solution is sought in the form of a linear combination of the delta-functions, whose positions and coefficients represent locations and weights of the particles.
Proceedings ArticleDOI
Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured-Grid Cell-Centered Finite-Volume Solver
TL;DR: A robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cell- average gradients is described and investigated and a comparison of least-squares stencil construction methodologies is presented.
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.