Journal ArticleDOI
FRAM—Nonlinear damping algorithms for the continuity equation
TLDR
In this article, a nonlinear filtering methodology for numerical solution of the convective terms in the Eulerian form of the hydrodynamic equations was developed for the multidimensional continuity equation and tested on several differencing schemes in both one and two spatial dimensions.About:
This article is published in Journal of Computational Physics.The article was published on 1981-11-01. It has received 88 citations till now. The article focuses on the topics: Nonlinear system & Independent equation.read more
Citations
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Journal ArticleDOI
Numerical advection algorithms and their role in atmospheric transport and chemistry models
TL;DR: In this paper, a review summarizes the development and improvements that have taken place and highlights the nature of the errors caused by numerical approximation to the advection equation and particular devices that have been proposed to remedy these errors.
Journal ArticleDOI
Normalized variable and space formulation methodology for high-resolution schemes
Marwan Darwish,Fadl Moukalled +1 more
TL;DR: In this paper, a new normalized variable and space formulation (NVSF) methodology is developed to derive connective schemes for uniformly or nearly uniformly discretized spaces, where spatial parameters are introduced so as to extend the applicability of the NVF methodology to nonuniformly discretised domains.
Journal ArticleDOI
A unified formulation of the segregated class of algorithms for fluid flow at all speeds
Fadl Moukalled,Marwan Darwish +1 more
TL;DR: In this paper, the segregated SIMPLE algorithm and its variants are reformulated, using a collocated variable approach, to predict fluid flow at all speeds in a unified, compact, and easy-to-understand notation.
Journal ArticleDOI
Transport theory for growing cell populations.
TL;DR: The partial differential equation that describes the growth of cell populations whose maturation rate is random is developed, a generalization of a previously published formulation in which cells could make transitions at random between only two maturation velocities.
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A comparison of numerical methods for solving the advection equation—III
TL;DR: In this paper, the authors compared four algorithms and their variations for solving the advection equation in terms of their accuracy, speed and storage requirements: the Smolarkiewicz method, the higher-degree-weighting Petrov-Galerkin method (HWPCG), the Taylor-Galerkin method, and the accurate-space-derivative method.
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
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.
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Flux-corrected transport II: Generalizations of the method
TL;DR: In this paper, the Lax-Wendroff, leapfrog, and upstreaming types of FCT are compared with one another and with some conventional FCT algorithms.
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Heuristic stability theory for finite-difference equations☆
TL;DR: In this article, a simple method is proposed for investigating the computational stability of finite-difference equations with variable coefficients, based on an examination of certain kinds of truncation errors, which is illustrated by applying it to a simple linear difference equation.
Journal ArticleDOI
Flux-corrected transport. III. Minimal-error FCT algorithms
Jay P. Boris,David L. Book +1 more
TL;DR: Improved FCT algorithms are found to be four to eight times more accurate than standard non-FCT algorithms, nearly twice as accurate as the original SHASTA FCT algorithm, and approach the accuracy of the optimal algorithm.
Related Papers (5)
Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works
Jay P. Boris,David L. Book +1 more