Unstructured Spectral Element Methods for Simulation of Turbulent Flows

Abstract

In this paper we present a spectral element-Fourier algorithm for simulating incompressible turbulent flows in complex geometries using unstructured quadrilateral meshes. To this end, we compare two different interface formulations for extending the conforming spectral element method in order to allow for surgical mesh refinement and still retain spectral accuracy: the Zanolli iterative procedure and variational patching based on auxiliary "mortar" functions. We present an interpretation of the original mortar element method as a patching scheme and develop direct and iterative solution techniques that make the method efficient for simulations of turbulent flows. The properties of the new method are analyzed in detail by studying the eigenspectra of the advection and diffusion operators. We then present numerical results that illustrate the flexibility as well as the exponential convergence of the new algorithm for nonconforming discretizations. We conclude with simulation studies of the turbulent cylinder wake at Re = 1000 (external flow) and turbulent flow over riblets at Re = 3280 (internal flow).