Wall‐modeled large‐eddy simulation in a finite element framework

This work studies the implementation of wall modeling for large‐eddy simulation in a finite element context. It provides a detailed description of how the approach used by the finite volume and finite differences communities is adapted to the finite element context. The new implementation is as simple and easy to implement as the classical finite element one, but it provides vastly superior results. In the typical approach used in finite elements, the mesh does not extend all the way to the wall, and the wall stress is evaluated at the first grid point, based on the velocity at the same point. Instead, we adopt the approach commonly used in finite differences, where the mesh covers the whole domain and the wall stress is obtained at the wall grid point, with the velocity evaluated at the first grid point off the wall. The method is tested in a turbulent channel flow at R e τ =2003, a neutral atmospheric boundary layer flow, and a flow over a wall‐mounted hump, with significant improvement in the results compared to the standard finite element approach. Additionally, we examine the effect of evaluating the input velocity further away from the walThis work was supported by the Energy oriented Centre of Excellence II (EoCoE‐II), grant agreement number 824158, funded within the Horizon2020 framework of the European Union. We would also like to acknowledge PRACE for awarding us access to the following resources: GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (www.lrz.de), Marconi at CINECA (http://www.hpc.cineca.it/), and TGCC Curie at CEA‐GENCI (http://www‐hpc.cea.fr). The authors thankfully acknowledges the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES‐AECT‐2018‐3‐0028).Peer ReviewedPostprint (author's final draft

Simulations of Unsteady Shocks via a Finite-Element Solver with High-Order Spatial and Temporal Accuracy

This research aims to improve the modeling of stationary and moving shock waves by adding an unsteady capability to an existing high-spatial-order, finite-element, streamline upwind/Petrov-Galerkin (SU/PG), steady-state solver and using it to examine a novel shock capturing technique. Six L-stable, first- through fourth-order time-integration methods were introduced into the solver, and the resulting unsteady code was employed on three canonical test cases for verification and validation purposes: the two-dimensional convecting inviscid isentropic vortex, the two-dimensional circular cylinder in cross ow, and the Taylor-Green vortex. Shock capturing is accomplished in the baseline solver through the application of artificial diffusion in supersonic cases. When applied to inviscid problems, especially those with blunt bodies, numerical errors from the baseline shock sensor accumulated in stagnation regions, resulting in non-physical wall heating. Modifications were made to the solver\u27s shock capturing approach that changed the calculation of the artificial diffusion flux term (Fad) and the shock sensor. The changes to Fadwere designed to vary the application of artificial diffusion directionally within the momentum equations. A novel discontinuity sensor, derived from the entropy gradient, was developed for use on inviscid cases. The new sensor activates for shocks, rapid expansions, and other ow features where the grid is insufficient to resolve the high-gradient phenomena. This modified shock capturing technique was applied to three inviscid test cases: the blunt-body bow shock of Murman, the planar Noh problem, and the Mach 3 forward-facing step of Colella and Woodward