THE BASIC EQUATIONS FOR THE LARGE-EDDY SIMULATION OF TURBULENT FLOWS IN COMPLEX-GEOMETRY

The equations for large eddy simulation (LES) of turbulent flows are d erived by applying a ''filtering'' operation to the Navier-Stokes equa tions. LES of inhomogeneous turbulent flows requires the use of filter s with variable filter width. The use of such filters invalidates the standard derivation of the basic equations for the filtered fields sin ce the filtering operation in general does not commute with the operat ion of differentiation. in this paper an alternate definition of the f iltering operation based on the mapping function of the nonuniform gri d is introduced. It is shown that with this modified definition the fi ltering and differentiation operations commute up to an error which is second order in the filter width. It is also shown that the commutati on error can be expressed in terms of the filtered field and its deriv atives as an asymptotic series in the square of the filter width. Thes e results are then applied to the Navier-Stokes equations to derive th e basic equations satisfied by the filtered fields. (C) 1995 Academic Press. Inc.