Derivation of Macroscale Equations for a Class of Physical Applications

摘要

A marcoscale formulation is constructed from a system of partial differential equations which govern the microscale dependent variables. The construction is based upon transformations of equations on second order contact manifolds under conditions of integrability. Necessary conditions on the structure of the macroscale equations are obtained under the requirement that the solutions of the macroscale equations satisfy, in some approximate sense, the equations associated with the microscale. This approach offers a method whereby one can construct only those macroscale equations that can be validated by a condition of consistency based on the model error. The methodology is employed to construct a turbulence closure model for incompressible flow. It is shown that the large eddy viscosity, which satisfies contemporary tests based on Galilean invariance, fails the consistency condition defined here.