DNS Simulations

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 [3] and Orlandi [4] 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 [4]. 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) [5] (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 1. Channel geometry with smooth wall

Figure 2. Channel geometry with pyramid roughness

Figure 3. Various unsteady flows simulated by the code

Test cases

i) smooth-wall, mild acceleration

Figure 4. History of the mild-acceleration
Figure 5. Development of wall shear stress during a mild accelleration

                     Figure 6. A movie for the mild-ramp simulation

ii) smooth-wall, fast acceleration

Ub-fast tau-fast lower-32


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.