zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Approximating the larger eddies in fluid motion. III: The Boussinesq model for turbulent fluctuations. (English) Zbl 1078.76553

Summary: In 1877 Boussinesq (and others) put forward the basic analogy between the mixing effects of turbulent fluctuations and molecular diffusion: -·(u ' u ' ) ¯-·ν T (u ¯+u ¯ t ). This assumption lies at the heart of essentially all turbulence models and subgridscale models. By revisiting the original arguments of Boussinesq, Saint-Venant, Kelvin, Reynolds and others, we give three new approximations for the turbulent viscosity coefficient ν T in terms of the mean flow based on approximation for the distribution of kinetic energy in u ' in terms of the mean flow u ¯. We prove existence of weak solutions for the resulting system (NSE plus the proposed subgridscale term). Finite difference implementations of the new eddy viscosity/subgrid-scale model are transparent. We show how it can be implemented in finite element procedures and prove that its action is no larger than that of the popular Smagorinski-subgrid-scale model.

Part II, cf. G. P. Galdi and W. J. Layton, Math. Models Methods Appl. Sci. 10, No. 3, 343–350 (2000; Zbl 1077.76522). Further parts have been reviewed in (V) Zbl 1042.76537.

MSC:
76F65Direct numerical and large eddy simulation of turbulence
76M20Finite difference methods (fluid mechanics)
76M10Finite element methods (fluid mechanics)