Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

An implicit finite difference method is presented for obtaining steady state solutions to the time dependent, conservative Euler equations for flows containing shocks. The method used the two-point differencing approach of Keller with dissipation added at supersonic points via the retarded density concept. Application of the method to the one-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions shows the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. It is shown that the scheme offers certain advantages over the more widely used three-point schemes, especially in regard to application of boundary conditions

Critical study of higher order numerical methods for solving the boundary-layer equations

A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows

Adaptation de maillage pour des modeles turbulents hybrides

International audienceThe purpose of our study is to propose the combination of a space-time anisotropic mesh adaptation with a novel hybrid RANS/LES modelization. We first discuss the design of an hybrid model able to address a sufficiently large class of flows around obstacles. A RANS model is enriched with an intermittency equation and associated with a LES model in some regions of the flow. Second, a strategy is proposed to adapt the mesh for a better capture of unsteady behaviors. The adaptation is metric based, space and time. The new methods are applied to flows around cylinders and airfoils.Le but de notre étude est de proposer la combinaison d’une adaptation de maillage anisotrope spatio-temporel avec une nouvelle modélisation hybride RANS/LES. Nous discutons d’abord de la conception d’un modèle hybride capable d’adresser une classe suffisamment large de flux autour d’obstacles. Un modèle RANS est enrichi d'une équation d'intermittence et associé à un modèle LES dans certaines régions de l'écoulement. Deuxièmement, une stratégie est proposée pour adapter le maillage afin de mieux capturer les comportements instables. L'adaptation est basée sur la métrique, l'espace et le temps. Les nouvelles méthodes sont appliquées aux écoulements autour des cylindres et des profils aérodynamiques

Assessment of turbulence hybrid models with transition modeling for the simulation of massively separated flows

International audienceIn the proposed communication, several hybrid turbulence models, possibly equipped with transition modeling, are evaluated on the simulation of the flow around a circular cylinder in the supercritical regime and over an airfoil at incidence. The flow through the Caradonna-Tung rotor will complete the benchmarks considered in this study. The first hybrid approach investigated in this work is the classical Delayed Detached Eddy Simulation (DDES) model. The two other hybrid models combine either a RANS model or the DDDES approach with a dynamic variational multiscale large eddy simulation (DVMS) model. A smooth blending function, which is based on the value of a blending parameter, is used for switching from RANS to DVMS in the RANS/DVMS strategy [1]. In the DDES/DVMS approach [2], the DVMS model is preferentially activated in the wake in order to more accurately predict this region of the flow thanks to the low dissipation introduced by this model. With the aim of improving the prediction of the targeted flows, a new kεγ transition model based on the model of Akhter [3] is also developped and used in these hybrid approaches. Results are compared to those of other RANS, LES and hybrid simulations in the literature and with experimental data, and highlight the overall good prediction capabilities of the proposed hybrid strategies for the simulation of such massively separated flows, with often a significant improvement when the transition model is activated