On the use of relaxation methods for localized dynamic models

An analogy with the use of relaxation methods is identified in both the Lagrangian dynamic model [J. Fluid Mech. 319, 353 (1996)] and the localized dynamic model [Phys. Fluids 7, 839 (1995)]. A general way to introduce a relaxation method for dynamic models is proposed, together with the ability of deriving constants without using Germano’s identity [Phys. Fluids A 3, 1760 (1991)]. The resulting family of models contains a relaxation parameter r a and leads to a strictly local and stable modeling, as shown by a posteriori tests in channel flow for Re τ =180. The influence of r a is briefly discussed.