Nicoletta Franchina

Very high-order accurate discontinuous Galerkin computation of transonic turbulent flows on aeronautical configurations

This chapter presents high-order DG solutions of the RANS and k-ω turbulence model equations for transonic flows around aeronautical configurations. A directional shock-capturing term, proportional to the inviscid residual, is employed to control oscillations around shocks. Implicit time integration is applied to the fully coupled RANS and k-ω equations. Several high-order DG results of 2D and 3D transonic turbulent test cases proposed within the ADIGMA project demonstrate the capability of the method.

Robust and Efficient Implementation of Very High-Order Discontinuous Galerkin Methods in CFD

Discontinuous Galerkin (DG) methods are a very powerful numerical techniques, that offer high degree of robustness, accuracy and flexibility, nowadays necessary for the solution of complex fluid flows. The drawback is the relatively high computational cost and storage requirement. This work will focus on two approaches which can be adopted to enhance the computational efficiency of this class of methods: (i) a DG discretization based upon co-located tensor product basis functions, and (ii) a p-multigrid solution strategy. The effectiveness of the proposed approaches has been demonstrated by computing 3D inviscid and turbulent test cases.

Assessment of a high-order accurate Discontinuous Galerkin method for turbomachinery flows

ABSTRACT In this work the capabilities of a high-order Discontinuous Galerkin (DG) method applied to the computation of turbomachinery flows are investigated. The Reynolds averaged Navier–Stokes equations coupled with the two equations k-ω turbulence model are solved to predict the flow features, either in a fixed or rotating reference frame, to simulate the fluid flow around bodies that operate under an imposed steady rotation. To ensure, by design, the positivity of all thermodynamic variables at a discrete level, a set of primitive variables based on pressure and temperature logarithms is used. The flow fields through the MTU T106A low-pressure turbine cascade and the NASA Rotor 37 axial compressor have been computed up to fourth-order of accuracy and compared to the experimental and numerical data available in the literature.

Discontinuous Galerkin computation of gaseous mixture coaxial jets

A novel approach based upon Discontinuous Galerkin (DG) discretization, applied to the divergence form of the multicomponent Navier-Stokes equations, is here presented and used to compute non reactive turbulent axisymmetric gaseous jets. The original key feature is the use of L2-projection form of the (perfect gas) equation of state. This choice mitigates problems typically encountered by the front-capturing schemes in computing multicomponent flow fields, i.e. spurious oscillations across material and contact surfaces where the mixture composition is changing. The solver makes also use of a shock-capturing technique based on artificial dissipation selectively added into the equations and tuned in connection with the magnitude of inviscid residuals of the equations and on suitable coefficients accounting for the variation of the unknown variables within and across grid elements. A simple limiting procedure is introduced in order to avoid the occurrence of unphysical gas properties due to negative and/or greater that one mass fractions values within the domain. The DG code based on the proposed novel technique for multicomponent flow computation is here employed to study the mixing mode and the preferential diffusion mechanism of a mixture jet of helium and carbon dioxide in a surrounding flow of air, both in laminar and turbulent flow regimes. Mass diffusion is modelled by means of Fick’s first law and use is made of constant Prandtl and Schmidt numbers in Wilcox’s (2008) k − ω model. Third-order accurate results are presented, discussed and compared with the available experimental data. They confirm the possible existence in coaxial jets of different periodic flow structures, greatly affecting mixing rates, and different species diffusive mass fluxes. The relative importance of both phenomena depends on the flow regime and its characteristics. The tests carried out give at the same time indications about the accuracy of the proposed method and its effectiveness in computing complex unsteady flow fields.