The simulation of flows over a wide range of spatial or temporal scales has turned out to be one of the most challenging and important fields in computational fluid dynamics. In order to study flow phenomena whose characteristics evolve on different scales or in the transition regime between the continuum, the statistical or the molecular scale, coupled multiscale methods are required. These hybrid methods represent a compromise between physical accuracy and computational complexity. Examples comprise molecular dynamics–Lattice Boltzmann simulations for nanoflows or hybrid continuum-statistical methods for rarefied gas flows where parts of the respective domains are solved by either coarse- or fine-scale simulation methods. For the development of these scale-coupling algorithms, accurate mathematical and physical models of the scale transition regime are required. Efficient sequential and parallel implementations of the single-scale components are necessary to solve the underlying flow problem in reasonable time. Besides, a well-fitting software environment needs to be chosen for the development of the single-scale solvers. One particular environment is given by Peano, a framework for spatially adaptive mesh-based simulations. Peano already contains a sophisticated Navier-Stokes solver for the study of continuum phenomena. Fine-scale simulation components-such as Lattice Boltzmann or molecular dynamics solvers-and respective coupled simulations, however, have not been integrated in the framework yet. Finally, the simulation software for the coupled multiscale system needs to provide a flexible and modular environment for the further development of new coupling strategies as well as an efficient and parallel treatment of the different coupling steps. In this thesis, a spatially adaptive Lattice Boltzmann scheme is incorporated into Peano and extends the applicability of the framework from the continuum to the statistical scale. A modular development of coupled algorithms is guaranteed via the design principles of Peano. The software is validated in benchmark computations and applied to micro- and nanoflow scenarios such as rarefied gas flows in microreactors or particle transport in nanopores. For the latter, an adaptive mesh refinement technique has been established which allows for the dynamic spatial refinement of particular flow regions. Besides, a new hybrid Lattice Boltzmann-Navier-Stokes method is presented and applied to the particle transport scenarios. In order to go beyond the statistical scale, a coupling tool for massively parallel molecular dynamics-Lattice Boltzmann simulations has been developed. Based on the analysis of existing coupling schemes, it encapsulates all coupling steps in different modules; this reduces the efforts in setting up new coupling schemes to the exchange of one or several available module implementations. To the author’s knowledge, the coupling tool hence provides the first piece of software for molecular dynamics-Lattice Boltzmann simulations with this high level of modularity on the one hand and applicability to massively parallel scenarios on the other hand. The capabilities of the tool are demonstrated in different molecular dynamics-Lattice Boltzmann scenarios.

@book{HMSAFMANN13,
	author	 = {Philipp Neumann},
	title	 = {{Hybrid Multiscale Simulation Approaches for Micro- and Nanoflows}},
	year	 = {2013},
	publisher	 = {Dr. Hut},
	address	 = {Munich},
	isbn	 = {978-3-8439-1178-8},
	abstract	 = {The simulation of flows over a wide range of spatial or temporal scales has turned out to be one of the most challenging and important fields in computational fluid dynamics. In order to study flow phenomena whose characteristics evolve on different scales or in the transition regime between the continuum, the statistical or the molecular scale, coupled multiscale methods are required. These hybrid methods represent a compromise between physical accuracy and computational complexity. Examples comprise molecular dynamics–Lattice Boltzmann simulations for nanoflows or hybrid continuum-statistical methods for rarefied gas flows where parts of the respective domains are solved by either coarse- or fine-scale simulation methods. For the development of these scale-coupling algorithms, accurate mathematical and physical models of the scale transition regime are required. Efficient sequential and parallel implementations of the single-scale components are necessary to solve the underlying flow problem in reasonable time. Besides, a well-fitting software environment needs to be chosen for the development of the single-scale solvers. One particular environment is given by Peano, a framework for spatially adaptive mesh-based simulations. Peano already contains a sophisticated Navier-Stokes solver for the study of continuum phenomena. Fine-scale simulation components-such as Lattice Boltzmann or molecular dynamics solvers-and respective coupled simulations, however, have not been integrated in the framework yet. Finally, the simulation software for the coupled multiscale system needs to provide a flexible and modular environment for the further development of new coupling strategies as well as an efficient and parallel treatment of the different coupling steps. In this thesis, a spatially adaptive Lattice Boltzmann scheme is incorporated into Peano and extends the applicability of the framework from the continuum to the statistical scale. A modular development of coupled algorithms is guaranteed via the design principles of Peano. The software is validated in benchmark computations and applied to micro- and nanoflow scenarios such as rarefied gas flows in microreactors or particle transport in nanopores. For the latter, an adaptive mesh refinement technique has been established which allows for the dynamic spatial refinement of particular flow regions. Besides, a new hybrid Lattice Boltzmann-Navier-Stokes method is presented and applied to the particle transport scenarios. In order to go beyond the statistical scale, a coupling tool for massively parallel molecular dynamics-Lattice Boltzmann simulations has been developed. Based on the analysis of existing coupling schemes, it encapsulates all coupling steps in different modules; this reduces the efforts in setting up new coupling schemes to the exchange of one or several available module implementations. To the author’s knowledge, the coupling tool hence provides the first piece of software for molecular dynamics-Lattice Boltzmann simulations with this high level of modularity on the one hand and applicability to massively parallel scenarios on the other hand. The capabilities of the tool are demonstrated in different molecular dynamics-Lattice Boltzmann scenarios.},
}