A fast numerical approach for the simulation of highly viscous non-isothermal non-Newtonian fluids

This paper deals with the efficient simulation of polymer melts, as an example of highly viscous non-isothermal non-Newtonian fluids. In flow fields of our interest, which are characterized by small Reynolds numbers and large Prandtl numbers, steep gradients occur in thin boundary layers of the temperature distribution, whereas the boundary layers associated with the velocity field possess a considerable different length scale. In order to benefit from these properties, we introduce a physically motivated multigrid approach by computing velocity and temperature fields on different meshes. This new development is achieved by the modification of a discrete projection method. Numerical experiments are presented which confirm that the method decreases the computational effort considerably, while preserving the numerical accuracy.