A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations

We present a semi-Lagrangian method for integrating the three-dimensional incompressible NavierStokes equations. We develop stable schemes of second-order accuracy in time and spectral accuracy in space. Specifically, we employ a spectral element (Jacobi) expansion in one direction and Fourier collocation in the other two directions. We demonstrate exponential convergence for this method, and investigate the non-monotonic behavior of the temporal error for an exact three-dimensional solution. We also present direct numerical simulations of a turbulent channel-flow, and demonstrate the stability of this approach even for marginal resolution unlike its Eulerian counterpart. ∗Corresponding author, [email protected]