Multiscale Simulation of Polymeric Fluids using Sparse Grids

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

A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions for kinetic simulations

The exact numerical simulation of plasma turbulence is one of the assets and challenges in fusion research. For grid-based solvers, sufficiently fine resolutions are often unattainable due to the curse of dimensionality. The sparse grid combination technique provides the means to alleviate the curse of dimensionality for kinetic simulations. However, the hierarchical representation for the combination step with the state-of-the-art hat functions suffers from poor conservation properties and numerical instability. The present work introduces two new variants of hierarchical multiscale basis functions for use with the combination technique: the biorthogonal and full weighting bases. The new basis functions conserve the total mass and are shown to significantly increase accuracy for a finite-volume solution of constant advection. Further numerical experiments based on the combination technique applied to a semi-Lagrangian Vlasov--Poisson solver show a stabilizing effect of the new bases on the simulations

Computational Multiscale Methods

Many physical processes in material sciences or geophysics are characterized by inherently complex interactions across a large range of non-separable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources by multiple orders of magnitude. The observation and prediction of physical phenomena from multiscale models, hence, requires insightful numerical multiscale techniques to adaptively select relevant scales and effectively represent unresolved scales. This workshop enhanced the development of such methods and the mathematics behind them so that the reliable and efficient numerical simulation of some challenging multiscale problems eventually becomes feasible in high performance computing environments

Computational Multiscale Methods

Computational Multiscale Methods play an important role in many modern computer simulations in material sciences with different time scales and different scales in space. Besides various computational challenges, the meeting brought together various applications from many disciplines and scientists from various scientific communities

The transformative potential of machine learning for experiments in fluid mechanics

The field of machine learning has rapidly advanced the state of the art in many fields of science and engineering, including experimental fluid dynamics, which is one of the original big-data disciplines. This perspective will highlight several aspects of experimental fluid mechanics that stand to benefit from progress advances in machine learning, including: 1) augmenting the fidelity and quality of measurement techniques, 2) improving experimental design and surrogate digital-twin models and 3) enabling real-time estimation and control. In each case, we discuss recent success stories and ongoing challenges, along with caveats and limitations, and outline the potential for new avenues of ML-augmented and ML-enabled experimental fluid mechanics