ISSN:
1572-9036
Keywords:
partial differential equations
;
contact manifolds
;
canonical transformations
;
turbulence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A macroscale formulation is constructed from a system of partialdifferential equations which govern the microscale dependent variables. Theconstruction is based upon transformations of equations on second ordercontact manifolds under conditions of integrability. Necessary conditions onthe structure of the macroscale equations are obtained under the requirementthat the solutions of the macroscale equations satisfy, in some approximatesense, the equations associated with the microscale. This approach offers amethod whereby one can construct only those macroscale equations that can bevalidated by a condition of consistency based on the model error. Themethodology is employed to construct a turbulence closure model forincompressible flow. It is shown that the large eddy viscosity, whichsatifies contemporary tests based on Galilean invariance, fails theconsistency condition defined here.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006008522273
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