An in-house DNS code [1,2] has been developed and is being using for the simulations. Various unsteady flows (periodic / non-periodic) can be studied by the code.
A standard second order finite difference method is used to discretise the spatial derivatives of the governing equations on a rectangular grid, where a three-dimensional staggered mesh is employed with a non-uniform spacing in the direction normal to the wall. The non-solenoidal intermediate velocity field is evaluated by means of a low storage third-order Runge–Kutta scheme for the non-linear terms together with a second order Crank–Nicholson scheme for the viscous terms. The time advancement of the Navier–Stokes equation is based on a fractional-step method described by Kim & Moin  and Orlandi  to enforce the solenoidal condition. The resulting discrete Poisson equation for the pressure is solved by an efficient 2-D FFT, taking advantage of an imposed periodicity in the streamwise and spanwise directions . The Message-Passing Interface (MPI) is used to parallelize the code for use on our distributed-memory computer clusters.
The code is adopted for simulations of 2-D roughness using an immersed boundary method (IBM)  (the corresponding subroutines are kindly provided by Professor Paolo Orlandi, University of Rome, Italy). The code is currently being revised to treat a 3-D pyramid roughness.
Figure 3. Various unsteady flows simulated by the code
i) smooth-wall, mild acceleration
Figure 4. History of the mild-acceleration
Figure 5. Development of wall shear stress during a mild accelleration
ii) smooth-wall, fast acceleration
1. M. Seddighi, Study of Turbulence and Wall Shear Stress in Unsteady Flow Over Smooth and Rough Wall Surfaces, PhD thesis, 2011.
2. M. Seddighi, S. He, P. Orlandi & A. Vardy, A comparative study of turbulence in a ramp-up and a ramp-down flow, Flow Turbulence and combustion, 86 (3-4), pp. 439-454, 2011.
3. Kim J, Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. Journal of Computational Physics 1985; 59(2):308-323.
4. Orlandi P. Fluid Flow Phenomena: A Numerical Toolkit. Kluwer, 2001.
5. Fadlun, E.A., Verzicco, R., Orlandi, P., & Mohd-Yusof, J. 2000. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 161, (1) 35-60.