Multiscale Simulation of Polymeric Fluids using Sparse Grids

Abstract

The numerical simulation of non-Newtonian fluids is of high practical relevance since most complex fluids developed in the chemical industry are not correctly modeled by classical fluid mechanics. In this thesis, we implement a multiscale multi-bead-spring chain model into the three-dimensional Navier-Stokes solver NaSt3DGPF developed at the Institute for Numerical Simulation, University of Bonn. It is the first implementation of such a high-dimensional model for non-Newtonian fluids into a three-dimensional flow solver. Using this model, we present novel simulation results for a square-square contraction flow problem. We then compare the results of our 3D simulations with experimental measurements from the literature and obtain a very good agreement. Up to now, high-dimensional multiscale approaches are hardly used in practical applications as they lead to computing times in the order of months even on massively parallel computers. This thesis combines two approaches to reduce this enormous computational complexity. First, we use a domain decomposition with MPI to allow for massively parallel computations. Second, we employ a dimension-adaptive sparse grid variant, the combination technique, to reduce the computational complexity of the multiscale model. Here, the combination technique is used in a general formulation that balances not only different discretization errors but also considers the accuracy of the mathematical model.