Design of a Variational Multiscale Method for High Reynolds Number Compressible Flows

Abstract

The ultimate goal of this work is the simulation of separated flow about the threedimensional FAITH bump to support Reynolds-averaged modeling efforts. Given the relatively high Reynolds number of this experimental configuration, numerical efficiency becomes paramount to enable practical simulations. This work describes the progress in the design of a VMM for high-Reynold-number separated flows, focusing on performance vs. accuracy trade-offs of the numerical schemes.

A Spectral-Element Approach for the Eikonal Equation

“…with f a known function with positive values, appears in many computational physics applications, including interface reinitialization [1][2][3], mesh generation [4][5][6], image segmentation [7, this formulation can be made independent of order of accuracy through the use of software optimization [19]. Adding the eikonal equation to this infrastructure can enable multiphase or fluid-structure interaction simulations, by providing an efficient and accurate signed-distance function.…”

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

“…The TGV was one of the problems in the 1st, 2nd and 3rd International Workshops on High-Order CFD Methods [38][39][40]) and is considered to be a challenging test for high-order methods. Various authors have used high-order discontinuous methods on the TGV test case with excellent results, including classical DG [5,36,37], DGSEM [9,29] and a preliminary study by Bull and Jameson using the FR-SD scheme [41]. Wang gives a review of the current status of high-order methods for several problems including the TGV [1].…”

“…by introducing artificial dissipation to represent the effect of the subgrid scales [20,[24][25][26][27][28]. A technique intended solely for stabilization of high-order schemes is over-integration, also known as polynomial de-aliasing, but this incurs a high computational cost [9,29]. Perhaps the simplest stabilization method, commonly utilized with second-order schemes, is upwinding of the interface fluxes for example by Roe's method [30].…”

“…Gassner [9], Diosady and Murman [29], Chapelier et al [5], Don et al [35], Johnsen et al [36] and Carton de Wiart et al [37]. The TGV was identified as a challenging problem for high-order methods in the 1st, 2nd and 3rd International Workshops on High-Order CFD Methods [38][39][40].…”

Scale-Resolving Simulations of Low-Pressure Turbine Cascades With Wall Roughness Using a Spectral-Element Method

“…The nonlinear system for each space-time slab is solved using a preconditioned Jacobian-free approximate Newton-Krylov solver. Further details regarding the space-time DG method can be found in [32][33][34][35]. Note also that no subgrid-scale or wall models are used in the present simulations.…”