Sparse grids - an approach to reduce the complexity of multiscale simulations

Abstract

A computationally efficient algorithm for multiscale simulations of non-Newtonian fluids is presented. This novel approach bases on a sparse grid discretization and extends previous simulations with a FENE dumbbell model in three-dimensional square-square contraction geometries. Multiscale simulations lead to model equations of high dimensionality. Depending on the number of spring segments, the configuration space for the polymer model has up to twenty dimensions. Therefore, multiscale simulations suffer from the curse of dimensionality and either require massively parallel computations or a problem-adapted approach such as sparse grids. In this talk, we compare our multiscale simulation with results from literature and obtain a good agreement. Furthermore, we demonstrate that our approach reduces the complexity of multiscale simulations by one order of magnitude.