By David L. Book (auth.), Dr. Dmitri Kuzmin, Prof. Rainald Löhner, Prof. Dr. Stefan Turek (eds.)
Addressing scholars and researchers in addition to CFD practitioners, this publication describes the state-of-the-art within the improvement of high-resolution schemes according to the Flux-Corrected delivery (FCT) paradigm. meant for readers who've a superior heritage in Computational Fluid Dynamics, the publication starts off with old notes via J.P. Boris and D.L. e-book. evaluate articles that stick with describe fresh advances within the layout of FCT algorithms in addition to a variety of algorithmic points. the subjects addressed within the e-book and its major highlights contain: the derivation and research of classical FCT schemes with specific emphasis at the underlying actual and mathematical constraints; flux restricting for hyperbolic platforms; generalization of FCT to implicit time-stepping and finite point discretizations on unstructured meshes and its function as a subgrid scale version for Monotonically built-in huge Eddy Simulation (MILES) of turbulent flows. The proposed improvements of the FCT method additionally include the prelimiting and 'failsafe' adjustment of antidiffusive fluxes, using attribute variables, and iterative flux correction. The reason and medication of harmful clipping/terracing results are mentioned. Many numerical examples are awarded for educational try difficulties and large-scale purposes alike.
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Additional resources for Flux-Corrected Transport: Principles, Algorithms, and Applications
Rotenberg, and J. ), Methods in Computational Physics, vol. 16 (Academic Press, New York, 1976). The Design of Flux-Corrected Transport (FCT) Algorithms For Structured Grids∗ Steven T. C. mil Summary. A given ﬂux-corrected transport (FCT) algorithm consists of three components: 1) a high order algorithm to which it reduces in smooth parts of the ﬂow; 2) a low order algorithm to which it reduces in parts of the ﬂow devoid of smoothness; and 3) a ﬂux limiter which calculates the weights assigned to the high and low order ﬂuxes in various regions of the ﬂow ﬁeld.
The Fi+(1/2) are called numerical ﬂuxes, and are functions of f and q at one or more of the time levels tn . The functional dependence of F on f and q deﬁnes the particular discrete approximation. As mentioned above, FCT constructs the net ﬂux Fi+(1/2) point by point and timestep by timestep (nonlinearly) as the weighted average of two ﬂuxes, one produced by a “high order” method and the other by a “low order” method. The formal procedure introduced in  is as follows: L , the “low order ﬂuxes,” using a method guaranteed not 1.
11) on a uniform mesh, that of using a leapfrog discretization in time and centered ﬁnite diﬀerences of arbitrary order in space. This choice allowed us to ignore the amplitude errors entirely, since for the leapfrog discretization these errors vanish for all k and for all ∆x and ∆t satisfying the Courant condition ≡ |u|∆t/∆x < 1. Further noting that the total phase error was the algebraic sum of that induced by the temporal and spatial discretizations separately, as long as both were small, we were able to reduce our algorithm analysis to a single plot, reproduced here in Fig.