Introduction to “Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works”
✍ Scribed by Steven T. Zalesak
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 120 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0021-9991
No coin nor oath required. For personal study only.
✦ Synopsis
Introduction to ''Flux-Corrected Transport. I. SHASTA, A Fluid Transport Algorithm That Works'' flux limiting. A more recent summary of FCT is given in In 1973, in the eighth year of its youth, the Journal the book by Oran and Boris . of Computational Physics published the classic Boris and Work on FCT algorithms has also thrived elsewhere Book paper describing flux-corrected transport (FCT) .
in publications far too numerous to reference here. Two Almost all of the monotonicity-preserving and nonoscillanotable examples are the extension of FCT to fully multiditory fluid transport algorithms of today trace their origins, mensional form in 1979 [8] and the generalization of FCT ultimately, to ideas that first appeared in this paper.
to unstructured grids (e.g., triangles and tetrahedra in two Boris and Book's new and far-reaching idea was to loand three dimensions, respectively) by Parrott and Christie cally replace formal truncation error considerations with in 1986 . One of the consequences of this last developconservative monotonicity enforcement in those places in ment has been the ability to perform FCT calculations in the flow where the formal truncation error had lost its extremely complex geometries. An example is the remarkmeaning, i.e., where the solution was not smooth and where able simulation of the World Trade Center blast which formally high order methods would violate physically motimodeled in detail the garage of the building including all vated upper and lower bounds on the solution. This is of the parked cars [10]. today still the fundamental principle underlying the great
The response of the scientific computing community to bulk of the monotonicity-preserving and nonoscillatory al-FCT was and still is remarkably strong. The original paper gorithms that have appeared in more recent times. Occaalone [1] has been cited 513 times, according to the ISI sionally this bit of history is lost in some of the more recent database. Even more telling is that 238 of these citations literature, in part due to the fact that the paper is now 24 were during the 1990s. This is an astounding total, given years old (and the original publication [2] older still). that these citations were all for a paper that was at least In , the authors applied this fundamental idea to a 17 years old at the time of the citation! Clearly the impact specific algorithm they termed SHASTA. They were able of this paper is still being felt long after its original publicato show not only sharp monotone advection of linear distion. FCT has been applied to virtually every area of scicontinuities, but also sharp nonoscillatory gasdynamic ence, from aerodynamics and shock physics to atmospheric shock waves. Included in [1] was a SHASTA calculation and ocean constituent transport, magnetohydrodynamics, of a shock tube problem much more difficult than that kinetic and fluid plasma physics, astrophysics, and compuused by Sod five years later [3], with nearly monotone tational biology. results and with no knowledge of the solution (e.g., Rie-Before releasing the reader to enjoy the paper, allow mann solvers) built in to the algorithm. All of these calculame to give a personal view of the relationship between tions were the first of their kind with monotonicity-preserv-FCT and the ''nonoscillatory upwind schemes'' that aping algorithms of greater than first-order accuracy. It was peared later, started by the pioneering work of Van Leer also in this paper that the term ''flux-limiting'' 50] ap- [11,. If one examines any of these upwind schemes he peared in print for the first time.
will find that, in addition to the machinery which makes In the years following 1973, Boris and Book and colthem upwind, they inevitably contain monotonicity conleagues published two more FCT papers in the Journal of straints or ''limiters'' whose function is identical to that of Computational Physics [4, 5], followed by a chapter in the the Boris-Book flux limiter: to impose monotone nonoscil-Methods in Computational Physics book series [6] that latory behavior where formally high order methods would summarized their work through 1976. These works refined do otherwise. Furthermore, the form of these limiters is their ideas, generalizing the algorithms to a larger class of quite similar to that of the original Boris-Book limiter, which SHASTA was just one member. Their emphasis was but of course, this is to be expected, given their common on the continuity equation as a scalar representative of goal. Van Leer, to whom these constraints are most often systems of conservations laws and on advective phase error attributed within the upwind context, clearly developed as a primary culprit in the elimination of the errors that his ideas independently (and within a year following those of Boris and Book), but given the earlier publication, it is remained after nonoscillatory behavior was eliminated via 170