Abstracts - KTH Mechanics

Solving turbulent wall flow in 2D using volume-penalization
on a Fourier basis
G.H.Keetels ∗ , H.J.H. Clercx ∗ and G.J.F. van Heijst ∗
The volume-penalization method proposed by Angot et al. 1 allows the use of
fast Fourier pseudospectral techniques to simulate turbulent wall flows (where periodic
boundary conditions are absent). Convergence checks with respect to spatial
resolution, time stepping and the penalization strength are presented where a challenging
dipole-wall collision simulation serves as a benchmark (which is obtained by
high-resolution simulations with a 2D Chebyshev pseudospectral method). In this
numerical experiment thin boundary layers are formed during the dipole-wall collision,
which subsequently detach from the boundary and (eventually) roll up and
form small-scale vortices. In particular, the vorticity filaments and small-scale vorticity
patches in the near wall region can possibly deteriorate the flow computation
yielding a flow evolution deviating from the benchmark solution 2 . The complexity of
such flows can be observed in figure 1 where vorticity contour plots are displayed of
a dipole collision with the no-slip boundary near the upper right corner of a square
domain. It is found that Gibbs oscillations have a minor effect on the flow dynamics.
As a consequence it is possible to recover the solution of the penalized Navier-Stokes
equations acceptably accurate using a high-order postprocessing technique 3 . Note
that it is possible to capture all the small-scale features in the vorticity field of the
oblique collision. Increasing the penalization strength results in a natural convergence
scenario in terms of vortex trajectories which is demonstrated for a normal collision in
figure 1. Solving the penalized Navier-Stokes equation on a Fourier basis is computationally
much cheaper than the classical Chebyshev Navier-Stokes solvers. Therefore
the potential of the approach is further examined by considering the statistical properties
of fully developed 2D turbulence in bounded domains with Reynolds numbers
substantially larger than previously possible.
Figure 1: Vorticity contour lines of an oblique collision computed with the penalization
method (left) and Chebyshev solver (right). Convergence in terms of increasing penalization
strength (from left to right) for a normal collision, penalization computation (dashed) and
Chebyshev result (solid).
∗Department of Physics, Eindhoven University of Technology , P.O. Box 513, 5600 MB Eindhoven,
The Netherlands
1Angot et al, Num. Math, 81, 497 (1999).
2Clercx and Bruneau,Comp. Fluids 35, 245 (2006).
3Tadmor & Tanner, Found. Comp. Math.,2, 155 (2002)
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