Spectral element simulations of laminar and turbulent flows in complex geometries

Abstract

Spectral element methods are high-order weighted residual techniques based on spectral expansions of variables and geometry for the Navier-Stokes and transport equations. Their success in the recent past in simulating flows of industrial complexity derives from the flexibility of the method to accurately represent nontrivial geometries while preserving the good resolution properties of the spectral methods. In this paper, we review some of the main ideas of the method with emphasis placed on implementation and data management. These issues need special attention in order to make the method efficient in practice, especially in view of the fact that high computing cost as well as strenuous storage requirements have been a major drawback of high-order methods in the past. Several unsteady, laminar complex flows are simulated, and a direct simulation of turbulent channel flow is presented, for the first time, using spectral element techniques.