Large Eddy Simulation of gravity currents with a high order DG method

Abstract

This work deals with Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of a turbulent gravity current in a gas, performed by means of a Discontinuous Galerkin (DG) Finite Elements method employing, in the LES case, LES-DG turbulence models previously introduced by the authors. Numerical simulations of non-Boussinesq lock-exchange benchmark problems show that, in the DNS case, the proposed method allows to correctly reproduce relevant features of variable density gas flows with gravity. Moreover, the LES results highlight, also in this context, the excessively high dissipation of the Smagorinsky model with respect to the Germano dynamic procedure.

A priori tests of a novel LES approach to compressible variable density turbulence

“…Notice that, as previously remarked, the model equations (compressible Navier-Stokes equations with gravity), their non dimensional formulation and the numerical discretization are the same as presented in [1] and [4], to which we refer for a complete description of the numerical method. Time integration has been performed with a five stages Strong Stability Preserving Runge-Kutta method described in [26].…”

“…The initial pressure distribution in the domain is computed assuming an hydrostatic pressure profile where the initial value at the top of the domain is imposed as in [4]. The initial datum for temperature is derived starting from density and pressure and using the equation of state.…”

“…The initial datum for temperature is derived starting from density and pressure and using the equation of state. Concerning the boundary conditions, the same slip boundary conditions as in [4] have been imposed. For the space discretization, the polynomial degree p = 7 was employed, which entailed a number of degrees of freedom per element equal to N p = (p + 1)(p + 2)/2 = 36.…”

“…[5], [9], [10]. In particular, a modal DG discretization is employed, along the lines discussed in detail in [1], which has already been validated for lock-exchange simulations in [4]. This framework allows to compute in a straightforward way the filtered quantities as a projection onto a polynomial space of lower dimension with respect to the one employed for the DNS.…”

Large eddy simulation of non-Boussinesq gravity currents with a DG method

“…The mathematical model we employ for the description of gravity currents is based on the compressible Navier-Stokes equations, filtered with the same procedure as in [1,8]. The filtering operator, which is denoted by •, is defined as the projection onto a space of piecewise polynomial functions of the same degree p of the piecewise polynomial basis functions used by the DG method.…”