Multiscale Large Eddy Simulation of Turbulence Using High-Order Finite Element Methods

Abstract

In this paper, multiscale large-eddy simulation (LES) is investigated using a high-order discontinuous Galerkin (DG) finite element method to study the instantaneous and statistical features of turbulent flows. In the present LES, large structures of the flow are directly resolved and simulated, while the effects arising from scales smaller than the grid size are accounted for by means of a wall-adapting local eddy-viscosity (WALE) model. This subgrid scale model is chosen for obtaining correct eddy-viscosity near-wall behavior and ease of implementation. To enhance the accuracy of LES solutions, the high-order DG method is used in conjuction with high-order implicit temporal schemes, varying from a second-order backward difference formula to a fourth-order implicit Runge-Kutta scheme. Curved surface representations are properly modeled through a computational analysis programming interface while the interior mesh is deformed subsequently via a linear elasticity solver for allowing valid anisotropic elements. Numerical results demonstrate the capabilities of the high-order LES-WALE algorithms for capturing both dynamic and statistical properties of turbulent flows. The employment of a higher-order discretization is also shown to be beneficial to resolving both mean flow and turbulence statistics, as well as improving the solution accuracy and computational efficiency. Furthermore, the order-of-accuracy property of the present high-order finite element method is assessed using the Method of Manufactured Solutions based on the compressible LES-WALE equations.

Finite Element Solutions for Turbulent Flow over the NACA 0012 Airfoil

“…Professors, research faculty, and students at the Chattanooga campus of the University of Tennessee have been developing highorder finite element capabilities for a wide range of applications including fluid dynamics, electromagnetics, and structural analysis [1][2][3][4][5][6][7][8][9]. Here, both discontinuous-Galerkin (DG) methods and PetrovGalerkin (PG) stabilized finite element methods have been pursued, and it has been clearly demonstrated that the PG approach has significant advantages over the DG approach in terms of the amount of computational work required for the same level of accuracy for moderate orders of accuracy [1,9,10].…”