A new Lattice Boltzmann collision model for large eddy simulation (LES) of weakly compressible flows is proposed. This model, referred to as the Hybrid Recursive Regularised Bhatnagar-Gross-Krook (HRR-BGK) model, is based on a modification of previously existing regularised collision models defined with the BGK Lattice Boltzmann method (LBM) framework. By hybridising the computation of the velocity gradient with an adequate Finite Difference scheme when reconstructing the non-equilibrium parts of the distribution function, a hyperviscosity term is introduced in the momentum equation, whose amplitude can be explicitly tuned via a weighting parameter. A dynamic version of the HRR-BGK is also proposed, in which the control parameter is tuned at each grid point and each time step in order to recover an arbitrarily fixed total dissipation. This new collision model is assessed for both explicit and implicit LES considering the flow around a circular cylinder at Re = 3900. The dynamic HRR-BGK is observed to yield very accurate results when equipped with Vreman's subgrid model to compute the target dissipation.

A thermal lattice Boltzmann model with a hybrid recursive regularization (HRR) collision operator is developed on standard lattices for simulation of subsonic and sonic compressible flows without shock. The approach is hybrid: mass and momentum conservation equations are solved using a lattice Boltzmann solver, while the energy conservation is solved under entropy form with a finite volume solver. The defect of Galilean invariance related to Mach number is corrected by the third order equilibrium distribution function, supplemented by an additional correcting term and hybrid recursive regularization. The proposed approach is assessed considering the simulation of i) an isentropic vortex convection, ii) a two dimensional acoustic pulse and iii) non-isothermal Gaussian pulse with Ma number in range of 0 to 1. Numerical simulations demonstrate that the flaw in Galilean invariance is effectively eliminated by the compressible HRR model. At last, the compressible laminar flows over flat plate at Ma number of 0.3 and 0.87, Reynolds number of 10 5 are considered to validate the capture of viscous and diffusive effects.