A second-order method for three-dimensional particle simulation

Pressure-driven flow in a channel with porous walls

“…As in our previous paper (Zhang & Prosperetti 2009), our numerical simulations are carried out using the physalis method which, for the present three-dimensional situation, is described in detail in Zhang & Prosperetti (2005). The method is essentially of the immersed boundary type, with an important twist.…”

“…For example, it was shown in Zhang & Prosperetti (2005) that, even at a Reynolds number of 50, the Stokes approximation is accurate up to distances of 10 % of the particle radius and beyond. As the Reynolds number increases, the region where this approximation is applicable shrinks, but is never zero.…”

Modelling microscale flow and colloid transport in saturated porous media

“…This is obtained by the method of separation of variables applied to Stokes flow equations. The general form in 2D is given in Zhang and Prosperetti (2003) and in 3D is found in Zhang and Prosperetti (2005) and Gao and Wang (2007). The second component is the numerical method for Navier-Stokes equations on a regular mesh (the flow solver).…”

Bubbles and particles in a cylindrical rotating flow

“…In this section we briefly explain our numerical method. We used the three-dimensional Navier-Stokes solver Physalis (Zhang and Prosperetti [70]). The underlying method rests on the observation that, owing to the no-slip condition, the flow in the immediate neighborhood of a particle differs at most slightly from a rigid-body motion and can therefore be linearized about such a motion.…”

“…This property eliminates the need to calculate these quantities by integration of the fluid stress over the particle surface. For details about this method the reader is referred to Zhang and Prosperetti [70] and for applications to Zhang, Botto, and Prosperetti [71].…”