Lagrangrian Methods for the Tensor-Diffusivity Subgrid Model

Graduate Aeronautical Laboratories
Caltech

Abstract-
In order to compute complex flows accurately, one needs a large computational effort to resolve both small and large length scales. By filtering the equations of motion, one ends up with equations for the large scale structures in which the effect of the small scales has to be modeled for closure. These models are called subgrid models.

Our research focussed on the filtered scalar advection-diffusion equation. For a Gaussian filter, an infinite series expansion for the advection term was found for closure. By retaining only the first two terms in the expansion, the tensor-diffusivity subgrid model is obtained. This model can be interpreted as a tensor-diffusivity term proportional to the rate-of-strain tensor of the large-scale filtered velocity field. In order to control negative diffusion in the stretching directions, a Lagrangian method is used.

The scalar field is represented in terms of a collection of anisotropic or axisymmetric Gaussian particles each with their own location and shape. Numerical results will be presented for chaotic 2D and 3D test flows. Good agreement with filtered direct numerical simulations and literature is obtained.

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