Couette and Poiseuille Flow

As a first test of the code, it was examined whether simple Couette and Poiseuille flow could be recovered. Figure 1 shows a spatially and temporally averaged flow field for the system undergoing Couette flow where the Lees–Edwards boundary condition is being imposed. The spatial averaging was done over a cubic array of bins with length 1 on a side. Due to the stochastic term in the DPD equations the instantaneous flow field will appear noisy, hence, the flow field was averaged over 100 separate time steps. The fluid viscosity was determined from the simulation by calculation of the stress tensor using Eqs. 12, 13. Next, Poiseuille flow was obtained by dividing the simulation cell in half and applying a body force in opposite directions in each cell half. Figure 2 shows the spatially and temporally averaged velocity profile in one cell after it had relaxed to its equilibrium profile. The solid line is a fit to the analytical solution of the Stokes equation with a similarly applied body force and a no slip boundary condition imposed at the cell boundaries. The only adjustable parameter in the fit was the fluid viscosity. The viscosity obtained from fitting these data was within a percent of that obtained from direct calculation of the stress tensor for the previously described Couette flow simulation, showing that the hydrodynamics was self consistent. As a corollary, this Poiseuille flow simulation demonstrates that a noslip boundary condition can be approximated, at a fluid-wall interface, by embedding a cell in the wall that is a mirror image of the adjacent fluid particles but with the velocities in the opposite direction. Although not exact, this is somewhat akin to the bounceback boundary condition used in lattice Boltzmann simulations [Rothman and Zaleski (1994)].

Fig. 2. Poiseuille flow obtained by applying a body force to the DPD fluid. An effective no-slip boundary condition is imposed at the walls. X is the position relative to the center of the cell. The circles are data representing the average local flow field from the simulation. The value of viscosity determined from a theoretical fit (solid line) for Poiseuille flow was consistent with direct calculation of the stress tensor from the Couette flow simulation in Fig. 1.