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

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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.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, Rhode Island, 02912

    Jin Xu, Dongbin Xiu & George Em Karniadakis

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  1. Jin Xu
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  2. Dongbin Xiu
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  3. George Em Karniadakis
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Xu, J., Xiu, D. & Karniadakis, G.E. A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations. Journal of Scientific Computing 17, 585–597 (2002). https://doi.org/10.1023/A:1015122714039

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  • DOI: https://doi.org/10.1023/A:1015122714039

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