LAUSR

Simple LB suffers fromnumerical instabilities when the collisional relaxation rate is reduced to model high Reynolds number turbulence (1). Various groups (2, 3) then introduced systematic entropic representationswhich satisfiedadiscreteH-theoremand thus led to stable numerical algorithms for Navier-Stokes (NS) turbulence. However, twomajor drawbacksbecame clear (4): (1) a Newton–Raphson iterative solver must be applied at every lattice node and at every time step in order to determine the entropy function isosurface; and (2) the entropic stabilizing factor directly effects the transport coefficient, leading to a time–space varying eddy transport coefficient. Recently, the Karlin group (3, 5) has developed an analytic entropy algorithm that leaves the viscosity ν invariant. It is based on a multiple relaxation LB model and the splitting of the distribution function fi into a moment-conserving ki set, a shear/stress si set and the remaining higher order set of moments hi. (There is a 1-1 onto map between the number of velocities and the number of moments). Thus the standard LB algorithm