Abstract

Discontinuous Galerkin methods have emerged in recent years as an alternative for nonlinear conservation equations. In particular, their inherent structure (a numerical flux based on a suitable approximate Riemann solver introduces some stabilization) suggests that they are specially adapted to capture shocks. However, numerical fluxes are not sufficient to stabilize the solution in the presence of shocks. Thus, slope limiter methods, which are extensions of finite volume methods, have been proposed. These techniques require, in practice, mesh adaption to localize the shock structure. This is is more obvious for large elements typical of high-order approximations. Here, a new approach based on the introduction of artificial diffusion into the original equations is presented. The order is not systematically decreased to one in the presence of the shock, large high-order elements can be used, and several linear and nonlinear tests demonstrate the efficiency of the proposed methodology.

Abstract

The aim of this work is to propose an hp-adaptive algorithm for discontinuous Galerkin methods that is capable to detect the discontinuities and sharp layers and avoid the spurious oscillation of the solution around them. In order to control the spurious oscillations, artificial viscosity is used with the particularity that it is only applied around the layers where the solution changes abruptly. To do so, a novel troubled-cell detector has been developed in order to mark the elements around those layers and to impose linear order in them. The detector takes advantage of the evolution of the value of the gradient through the adaptive process.

Abstract

Implicit large-eddy simulations of the high-pressure turbine cascade VKI-LS89 under transonic operating conditions using a high-order accurate discontinuous Galerkin spectral element method are presented. The subcell shock capturing method by Hennemann et al. [1] is investigated and compared against simulations with artificial viscosity. Additionally, the effect of laminar and turbulent inflow conditions are validated against numerical and experimental results from literature. This analysis shows that the subcell-shock-capturing method performs well by effectively reducing spurious oscillations across the shock front and acoustic waves while leaving the rest of the solution domain unaffected.

Abstract

In this work, a high-order implicit large-eddy simulation of an oblique shockwave/boundary layer interaction at Mach 2.3 is performed. The high-order solver is based on the flux reconstruction method, allowing an arbitrary order of accuracy. A particular attention is paid to the shock-capturing technique which consists in a combination of a Laplacian artificial viscosity with the Ducros sensor. The ability of such a solver to accurately predict the flow features is assessed on both steady and unsteady fields. In particular, the typical lowfrequency motion of the reflected shock is reproduced. The shock-capturing methodology is proven to be efficient at resolving the shocks without damping the turbulence in the boundary layer. The results obtained give confidence in this solver to study in more details the shockwave/boundary layer interaction phenomenon and future work is focused on the analysis of the oscillatory turbulent field in the interaction region.