In this contribution, we present our new adaptive Lattice Boltzmann implementation within the Peano framework, with special focus on nanoscale particle transport problems. With the continuum hypothesis not holding anymore on these small scales, new physical effects-such as Brownian fluctuations-need to be incorporated. We explain the overall layout of the application, including memory layout and access, and shortly review the adaptive algorithm. The scheme is validated by different benchmark computations in two and three dimensions. An extension to dynamically changing grids and a spatially adaptive approach to fluctuating hydrodynamics, allowing for the thermalisation of the fluid in particular regions of interest, is proposed. Both dynamic adaptivity and adaptive fluctuating hydrodynamics are validated separately in simulations of particle transport problems. The application of this scheme to an oscillating particle in a nanopore illustrates the importance of Brownian fluctuations in such setups.

@article{ADMRTFLBSO13,
	author	 = {Philipp Neumann and Tobias Neckel},
	title	 = {{A dynamic mesh refinement technique for Lattice Boltzmann simulations on octree-like
      grids}},
	year	 = {2013},
	editor	 = {Peter Wriggers},
	publisher	 = {Springer},
	journal	 = {Computational Mechanics},
	series	 = {51(2)},
	pages	 = {237--253},
	issn	 = {0178-7675},
	doi	 = {http://dx.doi.org/10.1007/s00466-012-0721-y},
	abstract	 = {In this contribution, we present our new adaptive Lattice Boltzmann implementation
      within the Peano framework, with special focus on nanoscale particle transport problems. With
      the continuum hypothesis not holding anymore on these small scales, new physical effects-such
      as Brownian fluctuations-need to be incorporated. We explain the overall layout of the
      application, including memory layout and access, and shortly review the adaptive algorithm.
      The scheme is validated by different benchmark computations in two and three dimensions. An
      extension to dynamically changing grids and a spatially adaptive approach to fluctuating
      hydrodynamics, allowing for the thermalisation of the fluid in particular regions of interest,
      is proposed. Both dynamic adaptivity and adaptive fluctuating hydrodynamics are validated
      separately in simulations of particle transport problems. The application of this scheme to an
      oscillating particle in a nanopore illustrates the importance of Brownian fluctuations in such
      setups.},
}