Direct Numerical Simulation of Particle-Laden Electrokinetic Flows on High Performance Computers

Computer simulations have become a powerful means to predict, analyze, and optimize the behavior of complex processes and systems. Nevertheless, the development of models and algorithms for multiphysics simulations that incorporate and couple multiple physical effects remains a challenging task. Moreover, multiphysics simulations of realistic scenarios with up to millions of interacting particles often require parallel supercomputers.

In this thesis, efficient algorithms for physically accurate, massively parallel multiphysics simulations of particle-laden electrokinetic flows on advanced high performance computers are presented. These fully parallelized, coupled algorithms are implemented within the software framework WALBERLA in a modular fashion. The modular software design ensures flexibility in the coupling of different algorithms, and extensibility for the implementation of more detailed or additional models. Excellent computational performance and parallel scalability are achieved by a careful parallel implementation and performance optimizations.

For direct numerical simulations of fluid-particle interactions, a lattice Boltzmann algorithm modeling the fluid flow is coupled to a computational model of rigid body dynamics for geometrically fully resolved particles. The coupled electric effects are modeled by electric potentials represented by a finite volume discretization on a mesh conforming to the lattice Boltzmann grid. For solving the electric potential equations and elliptic partial differential equations modeling other physical effects, WALBERLA is augmented by efficient parallel iterative solvers and by new boundary condition handling functionality.

The coupled models and their implementation are systematically validated, and the correctness of the overall multiphysics algorithms for electrokinetic flows with charged or uncharged particles in the presence or absence of ions in the fluid is verified. Moreover, the fluid-particle interaction is validated for spherical and elongated particles, and the tumbling motion of spherocylinders in the viscous flow regime is examined. In the validation experiments, the influence of several simulation parameters on physical accuracy is studied. Benchmark scenarios demonstrate the suitability of the different multiphysics algorithms for real-world applications.

To show the outstanding parallel performance of the algorithms for the simulation of millions of charged particles in fluid flow, their parallel scaling and numerical efficiency are analyzed on an advanced supercomputer.