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A detailed description of GENE-3D, a newly developed global stellarator version of the well established gyrokinetic turbulence code GENE, is provided – along with some initial simulation results. First, the underlying gyrokinetic equations and the use of field-aligned coordinates in non-axisymmetric magnetohydrodynamic equilibria are discussed. Then, various aspects regarding the numerical implementation in GENE-3D are described. Finally, the code is validated and its parallel performance is assessed, along with the influence of numerical precision.

The impact of dynamic models for applications to LES of compressible flows is assessed in the framework of a numerical model based on high order discontinuous finite elements. The projections onto lower dimensional subspaces associated with lower degree basis functions are used as LES filter, along the lines proposed in Variational Multiscale templates. Comparisons with DNS results available in the literature for plane and constricted channel flows at Mach numbers 0.2, 0.7 and 1.5 show clearly that the dynamic models are able to improve the prediction of most key features of the flow with respect to the Smagorinsky models employed so far in a VMS-DG context.

We propose a new, energy conserving, spectral element, discontinuous Galerkin method for the approximation of the Vlasov–Poisson system in arbitrary dimension, using Cartesian grids. The method is derived from the one proposed in [4] , with two modifications: energy conservation is obtained by a suitable projection operator acting on the solution of the Poisson problem, rather than by solving multiple Poisson problems, and all the integrals appearing in the finite element formulation are approximated with Gauss–Lobatto quadrature, thereby yielding a spectral element formulation. The resulting method has the following properties: exact energy conservation (up to errors introduced by the time discretization), stability (thanks to the use of upwind numerical fluxes), high order accuracy and high locality. For the time discretization, we consider both Runge–Kutta methods and exponential integrators, and show results for 1D and 2D cases (2D and 4D in phase space, respectively).

We investigate the possibility of reducing the computational burden of LES models by employing local polynomial degree adaptivity in the framework of a high order DG method. A novel degree adaptation technique especially featured to be effective for LES applications is proposed and its effectiveness is compared to that of other criteria already employed in the literature. The resulting locally adaptive approach allows to achieve significant reductions in computational cost of representative LES computations., 39 pages, 10 figures, 5 tables

The Hybrid RANS/LES method proposed is based on the hybrid filter approach introduced by Germano in 2004. In this work, instead of using two explicit models respectively for LES and RANS, we use only a model for LES and we reconstruct the RANS field exploiting the properties of hybrid filter. The reconstruction is obtained from the resolved velocity and the LES subgrid stress tensor. The model has been implemented using a variational approach in a DG-FEM framework and tested for the turbulent channel flow test case. Different configurations for hybrid terms have been compared with DNS data and with pure LES results.