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Multiscale simulation of polymeric fluids using the sparse grid combination technique

: Rüttgers, Alexander; Griebel, Michael


Applied mathematics and computation 319 (2018), pp.425-443
ISSN: 0096-3003
Journal Article
Fraunhofer SCAI ()

We present a computationally efficient sparse grid approach to allow for multiscale simulations of non-Newtonian polymeric fluids. Multiscale approaches for polymeric fluids often involve model equations of high dimensionality. A conventional numerical treatment of such equations leads to computing times in the order of months even on massively parallel computers. For a reduction of this enormous complexity, we propose the sparse grid combination technique. Compared to classical full grid approaches, the combination technique strongly reduces the computational complexity of a numerical scheme but only slightly decreases its accuracy. Here, we use the combination technique in a general formulation that balances not only different discretization errors but also considers the accuracy of the mathematical model. For an optimal weighting of these different problem dimensions, we employ a dimension-adaptive refinement strategy. We finally verify substantial cost reductions of our approach for simulations of non-Newtonian Couette and extensional flow problems.