In order to properly address the simulation of complex (weaklycompressible) turbulent flows, the lattice Boltzmann method, originally designed for uniform structured grids, needs to be extended to composite multi-domain grids displaying various levels of spatial resolution. Therefore, physical conditions must be specified to determine the mapping of statistical information (about the populations of moving particles) at the interface between two domains of different resolutions. quite simply in terms of the probability distributions of the underlying discrete-velocity Boltzmann equation. Namely, the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions, where as the discontinuity of the rate-of-strain tensor is ensured by applying a “spatial transformation” to the collision term of the discrete-velocity Boltzmann equation. The latter condition allows us to explicitly account for the subgrid-scale modeling in the treatment of resolution changes.
Test computations of a turbulent plane-channel flow have been carried out.
The lattice Boltzmann scheme relies on the standard D3Q19 lattice in a cell-vertex representation, and uses the BGKapproximation for the collision term. A shear-improved variant of the Smagorinsky viscosity is used to account for possible subgrid-scale dynamics. In a quasi-direct numerical simulation at Re=180 with two levels of grid resolution,the results are found in excellent agreement with reference data obtained by a high-resolution pseudo-spectral simulation. In a Large-Eddy Simulation (LES) a t Re = 395 with three levels of grid resolution, the results compare reasonably well with high-resolution reference data. The accuracy is improved in comparison with a standard finite-volume LES performed with the same subgrid-scale viscosity and comparable grid resolution.
By combining the simplicity and physical relevance of the shear-improved Smagorinsky model and the computational efficiency of the lattice Boltzmann scheme, here extended to composite multi-resolution grids, we believe that our proposal offers a high potential for the simulation of complex turbulent flows.