Comparison of a spectral method with volume penalization and a finite volume method with body fitted grids for turbulent flows

•Volume penalization pseudo-spectral code is applied to a flow over a periodic hill.•Penalization and finite volume methods reproduce well turbulent flow statistics.•Penalization is a powerful and flexible technique to consider complex geometries.•Scale-dependent statistics are analyzed using orthogonal wavelets.•Te influence of the Reynolds number is investigated for the Fourier pseudo-spectral scheme. We consider a turbulent flow past periodic hills at Reynolds number 1400 and compare two numerical methods: A Fourier pseudo–spectral scheme with volume penalization to model the no-slip boundary conditions and a finite volume method with body fitted grids. A detailed comparison of the results is presented for mean velocity profiles and Reynolds stress and confronted with those obtained by Breuer et al., [1]. In addition higher order statistics are performed and their scale-dependence is analyzed using orthogonal wavelets. Moreover, for the Fourier pseudo-spectral scheme, the influence of the Reynolds number is investigated.