The Navier-Stokes equations (NS) and the Lattice-Boltzmann method (LBM) are the main two types of models used in computational fluid dynamics yielding similar results for certain classes of flow problems both having certain advantages and disadvantages. We present the realization of both approaches-laminar incompressible NS and LB-on the same code basis, our PDE framework Peano. Peano offers a highly memory efficient implementation of all grid and data handling issues for structured adaptive grids. Using a common code basis allows to compare NS and LB without distorting the results by differences in the maturity and degree of hardware-optimality of thetechnical implementation. In addition to a comparison for some test examples, we briefly present the coupling of NS and LB in one single simulation. Such a coupling might be useful to simulate boundary effects happening on a smaller scale more accurately with LB but still using NS in the main part of the domain.

@article{NALBOOGITP11,
	author	 = {Miriam Mehl and Tobias Neckel and Philipp Neumann},
	title	 = {{Navier-Stokes and Lattice Boltzmann on octree-like grids in the Peano framework}},
	year	 = {2011},
	editor	 = {Remi Abgrall},
	publisher	 = {John Wiley \& Sons},
	journal	 = {International Journal for Numerical Methods in Fluids},
	series	 = {65(1-3)},
	pages	 = {67--86},
	issn	 = {0271-2091},
	doi	 = {http://dx.doi.org/10.1002/fld.2469},
	abstract	 = {The Navier-Stokes equations (NS) and the Lattice-Boltzmann method (LBM) are the main two types of models used in computational fluid dynamics yielding similar results for certain classes of flow problems both having certain advantages and disadvantages. We present the realization of both approaches-laminar incompressible NS and LB-on the same code basis, our PDE framework Peano. Peano offers a highly memory efficient implementation of all grid and data handling issues for structured adaptive grids. Using a common code basis allows to compare NS and LB without distorting the results by differences in the maturity and degree of hardware-optimality of thetechnical implementation. In addition to a comparison for some test examples, we briefly present the coupling of NS and LB in one single simulation. Such a coupling might be useful to simulate boundary effects happening on a smaller scale more accurately with LB but still using NS in the main part of the domain.},
}