Lagrangian Methods for the Tensor-Diffusivity Subgrid Model

A subgrid-scale model based on a truncated exact series expansion for Gaussian filtered products is considered for the incompressible scalar advection–diffusion equation. This model can be interpreted as a tensor diffusivity term proportional to the rate-of-strain tensor of the large-scale filtered velocity field. 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. An expansion in Hermite polynomials leads to equations of motion for particle velocity and shape based on a weighted average. A new accurate remeshing method, taking advantage of the properties of the subgrid model, is proposed and tested. A stagnation flow is used to demonstrate several theoretical and numerical aspects of the model. Better agreement with filtered DNS data is obtained than with the Smagorinsky subgrid model for a 2D time-dependent sinusoidal flow, which yields chaotic advection. The use of anisotropic particles leads to slightly more accurate results than the use of axisymmetric particles. Computational efficiency, however, makes the latter therefore the preferred choice.