### Synthetic field formulation for simulation of turbulent reacting flows

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Randall McDermott, University of Utah
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A numerical formulation is developed for large eddy simulation (LES) of a low Mach number, variable density reacting flow. Synthetic fields are used to close the nonlinear terms in the momentum and scalar equations. While these fields provide a nice model of convective transport they are ill suited to predict energy dissipation at the smallest scales. A new method of treating the viscous term is proposed whereby the subgrid volume region is viewed as an ensemble of laminar simple shear flows (“shearlets”). The governing equations are viewed in a finite volume formulation, where we introduce two different spatial filters, the volume filter and the surface filter. Volume filtered quantities are updated in the time integration. Surface filtered quantities are used in computing convective fluxes and surface forces. In this manner, the synthetic field need only be a two dimensional construct on the surface of the control volume. For this formulation to be practical, the synthetic field cannot be constructed explicitly. One must be able to directly integrate the model function in real space. The fractal interpolation technique provides a means for constructing such a field. It is proposed that the form of the synthetic field provides a means for constructing the subgrid probability density function of a scalar field. Several areas are identified where *a priori* testing with direct numerical simulation will be important in refinement of this formulation.

**Abstract Author(s): **Randall J. McDermott