Numerical simulation of electrorheological fluids based on an extended Bingham model

In the framework of the macroscopic simulation of electrorheological fluids, we present an extension of the classical Bingham model which goes beyond pure shear flows and thus enables the simulation of settings in more complex geometries. Emphasis is on the numerical solution of the resulting nonsmooth minimization problem. We propose the method of augmented Lagrangians combined with an operator-splitting technique which allows to confine the nonlinearity to local, low-dimensional problems. Numerical results are given that illustrate the electrorheological effects for various shear rates and electric field strengths in case of an electrorheological suspension rotating between two revolving cylinders.