A Lagrangian particle advection scheme for hybrid LES/FDF methods based on a mean velocity reconstruction with desirable divergence properties

Randall J. McDermott^{*}
and Stephen B. Pope

Cornell University

We describe a Lagrangian particle advection scheme for hybrid finite-volume (FV) large-eddy simulation/filtered density function (LES/FDF) methods. A key ingredient of the scheme is the reconstruction of a mean subgrid velocity field with desirable divergence properties. We develop reconstructions for 2D and 3D Cartesian staggered grids. The divergence of the mean subgrid velocity field is identical to the FV divergence at the mass control-volume cell center and varies linearly within the cell, attaining desirable limiting values at the cell vertices and edges. In the velocity component direction the subgrid velocity field is continuous and piecewise parabolic from cell to cell. A second-order Runge-Kutta advection scheme is employed that effectively smoothes any cell-to-cell discontinuities in the divergence and cross-directional velocities (e.g., the $u_1$ component in the $x_2$ direction). To assess the performance of the scheme we utilize analytical solutions to the Euler equations. It is shown that subgrid particle position distribution remains consistent with the mean mass density (taken from a highly accurate baseline numerical solution) in the particle-tracking limit.

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^{*}Current author information:

Postdoctoral Research Associate

National Institute of Standards and Technology

Mentor: William (Ruddy) Mell

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Category: (Computational) Physics; (equally, Mechanical Engineering or Applied Mathematics)