Abstract
Using a variant of a spectral collocation method we numerically solve the problem of the motion of a highly viscous fluid with pressure dependent viscosity under a surface load, which is a problem relevant in many applications, in particular in geophysics and polymer melts processing. We compare the results with the results obtained by the classical Navier-Stokes fluid (constant viscosity).
It turns out that for a realistic parameter values the two models give substantially different predictions concerning the motion of the free surface and the velocity and the pressure fields beneath the free surface. As a byproduct of the effort to test the numerical scheme we obtain an analytical solution for the classical Navier-Stokes fluid of the surface load problem in a layer of finite depth.