A wave propagation algorithm for viscoelastic fluids with spatially and temporally varying properties

An algorithm is presented for simulating the fluid and stress equations that arise in a continuum model of platelet aggregation [A.L. Fogelson, R.D. Guy, Platelet–wall interactions in continuum models of platelet thrombosis: formulation and numerical solution, Math. Med. Biol. 21 (2004) 293–334]. The model is equivalent to models of viscoelastic fluids with spatially and temporally varying material parameters. A subsystem containing the elastic terms is handled using a wave propagation algorithm. Two different methods for propagating waves are compared in computational tests. One method linearizes the equations about cell edges, and the other is based on the propagation of waves in a heterogeneous elastic medium. When the viscoelastic fluid is in contact with a Newtonian fluid, the method based on linearization about the edges gives more accurate results. No high Weissenberg number instabilities were observed. As long as the time step is chosen to obey a CFL condition, the algorithm is stable and no unphysical oscillations appear in the solution.