Large-Eddy Simulation Using Projection onto Local Basis Functions

Abstract

In the traditional approach to LES for inhomogeneous flows, the resolved fields are obtained by a filtering operation (with filter width Δ). The equations governing the resolved fields are then partial differential equations, which are solved numerically (on a grid of spacing h). For an LES computation of a given magnitude (i.e., given h), there are conflicting considerations in the choice of Δ: to resolve a large range of turbulent motions, Δ should be small; to solve the equations with numerical accuracy, Δ should be large. In the alternative approach advanced here, this conflict is avoided. The resolved fields are defined by projection onto local basis functions, so that the governing equations are ordinary differential equations for the evolution of the basis-function coefficients. There is no issue of numerical spatial discretization errors. A general methodology for modelling the effects of the residual motions is developed. The model is based directly on the basis-function coefficients, and its effect is to smooth the fields where their rates of change are not well resolved by the basis functions. Demonstration calculations are performed for Burgers’ equation.