An explicit finite difference scheme with spectral boundary conditions for particulate flows

We present an explicit finite difference scheme for solving two-dimensional particulate flow problems with a special treatment of the boundary conditions on the particle surface based on spectral solutions to the Stokes equations. This scheme allows for accurate solution of particulate flows up to a particle Reynolds number of one hundred on coarse grids (10–20 grid spacings per particle diameter). The coarse grid provides additional computational benefit by allowing for larger time steps required by the stability constraint. The method is validated and demonstrated through a number of examples, which include flow over a stationary cylinder, a cylinder moving with constant velocity, sedimentation of a free particle, the drafting, kissing, and tumbling of two particles, and 248 particles falling in a closed box.