Lagrangian averaged Navier–Stokes α turbulence model for compressible flows part I: Model derivation

In this paper, we extend the Lagrangian Averaged Navier–Stokes [Formula: see text] turbulence model to a calorically perfect, compressible fluid. The model is based on a free energy Lagrangian and viscosity is introduced as a constraint. We expand dependent variables in a series parameterized by the largest deviation of a particle trajectory from its statistical average location. The expansions are substituted into the Lagrangian and then averaged over trajectories. We apply Hamilton’s principle to create a system of equations and use Taylor’s hypothesis to close the system. The resultant equations are expressed in conservation form in Eulerian coordinates for use in computational fluid dynamics algorithms.