On the use of adaptive relaxation times in lattice Boltzmann methods

The lattice Boltzmann collision model with multiple relaxation times is modified to make the relaxation rates dependent on the shear stress. With these adaptive relaxation times, the optimal choice made by the theoretical development of MRT does not hold anymore. However, it is shown that the numerical properties of the collision model remains close to the MRT model. In particular, it is shown that the adaptive model recovers the BGK properties in terms of acoustical dissipation but keeps the numerical stability of MRT when shear stress becomes high. Then the adaptive model is studied in terms of stability and accuracy on the Taylor-Green vortex case, and the acoustic properties are tested on the sound radiated by a square cylinder.