High-order Methods for Solutions of Three-dimensional Turbulent Flows

Abstract

This paper presents a high-order discontinuous Galerkin (DG) method for three-dimensional turbulent flows. As an extension of our previous work, the paper further investigates the incorporation of a modified Spalart-and-Allmaras (SA) turbulence model with the Reynolds Averaged Navier-Stokes (RANS) equations that are both discretized using a modal discontinuous Galerkin approach. The resulting system of equations, describing the conservative flow fields as well as the turbulence variable, is solved implicitly by an approximate Newton approach with a local time-stepping method to alleviate the initial transient effects. In the context of high-order methods, curved surface mesh is generated through the use of a CAPRI mesh parameterization tool, followed by a linear elasticity solver to determine the interior mesh deformations. The requirements for the wall coordinate and viscous stretching factor used for viscous mesh generation are studied on a twodimensional turbulent flow case. It has been concluded that, for attached turbulent flows, the conventional parameters often used in low-order methods can be somewhat less stringent when a higher-order method is considered. Several other numerical examples including a direct numerical simulation of the Taylor-Green vortex and turbulent flow over an ONERA M6 wing are considered to assess the solution accuracy and to show the performance of high-order DG methods in capturing transitional and turbulent flow phenomena.

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].…”

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

“…The multiscale problems, however, have become more tractable for high-order computational methodologies due to the capabilities in achieving high accuracy with a significantly reduced mesh resolution. To this end, the current work continues on the development of a discontinuous Galerkin discretization method [3][4][5][6][7][8] to further expand the application areas of the high-order computational algorithms in large-eddy simulation of turbulent flow. Research effort is also placed on assessing the solution accuracy and computational efficiency, and demonstrating the performance of various orders of spatial and temporal schemes in LES applications.…”

“…High-order accurate computational methods such as discontinuous Galerkin (DG) finite element methods [1][2][3][4][5] have gained increasing popularity owing to the essential accuracy advantage for a given mesh resolution over the traditional second-order schemes. The accurate numerical simulation for complex systems, such as broadband noise source prediction, combustion instabilities, turbulence and transition, has posed a big challenge for the conventional low-order methods.…”

A Direct Discontinuous Galerkin Method for Computation of Turbulent Flows on Hybrid Grids

“…Instead of using two-equation k-ω model, more researchers incline to apply the one-equation SA model probably due to its successful application among traditional finite volume community and its simplicity in implementation. Burgess et al [21] and Wang et al [22] implemented high-order DG methods for solving a fully coupled RANS-SA system. In their work, a modified SA model is adopted and SIP method is used for the discretization of viscous flux.…”