Development of a Spectral Element DNS/LES Method for Turbulent Flow Simulations

Abstract

This paper describes a turbulent flow simulation method, which is based on combination of spectral element and large eddy simulation (LES) technique. The robust, high-order discontinuous Galerkin (DG) spectral element method for large-eddy simulation of compressible flows allows for arbitrary order of accuracy and has excellent stability properties. A local spectral discretization in terms of Legendre polynomials is used on each element of the (possibly unstructured) mesh, which allows for high-accurate simulations of turbulent flows. Discontinuities across the interfaces of the elements are resolved using a Riemann solver. An isoparametric representation of the geometry is implemented, with boundaries of the domain discretized to the same order of accuracy as the solution, and explicit low-storage Runge-Kutta methods are used for time integration. Large eddy simulation has proven to be a valuable technique for the calculation of turbulent flows. An element based filtering technique is used in conjunction with the standard Smagorinsky eddy viscosity model to estimate the effect of sub-grid scales stresses in this paper. The recently developed nonlinear model [1] will also be added in the future. The final aim of this project is to use the LES methodology in swirling jet flow simulation. As a first step towards these simulations, simulations of compressible turbulent mixing layer and back-facing step are also performed to evaluate the robust method. Initial results based on both DNS and large eddy simulations are presented in this paper. Future work will be to validate the code.