Seminar CCCS: Prof. M. Griebel (University of Bonn)

Dimension-adaptive sparse grid simulations of multiscale viscoelastic flows

Polymeric viscoelastic fluids can be modelled by using the Navier-Stokes equations on the macroscopic scale with an additional stress tensor and a higher-dimensional Fokker-Plank equation or a corresponding stochastic PDE on the microscopic scale. Here, the dimension of the microscopic problem is 3N where N+1 is the number of beads in the underlying spring bead model for viscoelasticity. For the numerical treatment of the overall system, we couple the the stochastic Brownian configuration field method with our fully parallelized three-dimensional Navier-Stokes solver NaSt3DGPF. But due to the microscopic problem, we directly encounter the curse of dimensionality. To this end, we suggest the so-called dimension-adaptive sparse grid approach. It allows to deal with moderate-sized subproblems in an adaptive fashion. Furthermore, all arising subproblems can be treated fully in parallel. This way, reliable multiscale simulations of viscoelastic flow problems for microscopic models with N>1 get possible for the first time. This is  joint work with Alexander Rüttgers from Bonn.

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