Abstract
A time discretization scheme based on the third-order backward difference formula has been embedded into a Chebyshev tau spectral method for the Navier–Stokes equations. The time discretization is a variant of the second-order backward scheme proposed by Krasnov et al. (2008) [3]. High-resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the Runge–Kutta scheme proposed by Spalart et al. (1991) [2]. It is shown that the Runge–Kutta scheme leads to a poor convergence of some third-order spatial derivatives in the direct vicinity of the wall, derivatives that represent the diffusion of wall-tangential vorticity. The convergence at the wall is shown to be significantly improved if the backward scheme is applied.
Original language | Undefined |
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Pages (from-to) | 162-169 |
Number of pages | 8 |
Journal | Journal of computational physics |
Volume | 304 |
DOIs | |
Publication status | Published - 1 Jan 2016 |
Keywords
- EWI-27486
- DNS of turbulent channel flow
- Navier–Stokes equations
- Chebyshev tau method
- METIS-320909
- IR-103050
- Multistep time discretization