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

Authors:
Jin Xu;Dongbin Xiu;George Em Karniadakis
Affiliations:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912;Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912;Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912. gk@cfm.brown.edu
Venue:
Journal of Scientific Computing
Year:
2002

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Abstract

We present a semi-Lagrangian method for integrating the three-dimensional incompressible Navier–Stokes 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.