Large eddy simulation with direct resolution of subgrid motion using a grid free vortex particle method

Theoretical Background of the Hybrid VπLES Method for Flows with Variable Transport Properties

“…We classified the method as the Large Eddy Simulation (LES) with a direct resolution of the subgrid (SG) motion modeled by u v part. Numerical simulations [2,3] showed that vortex particles play a role as triggers or intensifiers of the turbulence in the grid based solution. Their inner interaction does not contribute sufficiently to the flow evolution.…”

“…In our previous works [1][2][3] we propose a novel numerical technique, referred to as the VπLES approach, which utilizes the combination of grid based and grid free computational methods. The large scale motions are modeled on the grid whereas the fine scales are represented by vortex particles.…”

“…Due to inherent instability of turbulent flows, the grid based solution shows the tendency to create flow structures with sizes comparable with the cell size. In grid based methods, these structures either disappear due to artificial viscosity in schemes with a low order accuracy or result in a high frequency instability which is well seen in the spectra as a pile up of the kinetic energy at high frequencies [2] when high order schemes are utilized. Within the framework of VπLES such structures are recognized and converted to vortex particles which don't depend on the grid.…”

“…The algorithm for determination of the strengths of the vortex particles inducing u ω (x, t) (see [2,3]) is based on the identification of vortex structures in the field u (x, t) using the λ ci criterium [5] which is directly extendable to compressible flows [6]. At locations of large λ ci values we insert new vortex particles with the strength being equal to the local vorticity…”

“…old and a special rescaling procedure was introduced to match both velocities ( [2,3]). From the physical point of view u ε (x, t) arises due to the temporal change of the density fluctuation.…”