We present an Anderson acceleration-based approach to spatially couple three-dimensional Lattice Boltzmann and Navier-Stokes (LBNS) flow simulations. This allows to locally exploit the computational features of both fluid flow solver approaches to the fullest extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for the simultaneous execution of both Lattice Boltzmann and Navier-Stokes solver. We detail our coupling methodology, validate it, and study convergence and accuracy of the Anderson accelerated coupling, considering three steady-state scenarios: plane channel flow, flow around a sphere and channel flow across a porous structure. We find that the Anderson accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40% in the considered scenarios, compared to strictly sequential Schwarz coupling.

@article{SAACOLBANS16,
	author	 = {Atanas Atanasov and Benjamin Uekermann and Carlos A. Pachajoa Mejia and Hans-Joachim Bungartz and Philipp Neumann},
	title	 = {{Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier-Stokes Solvers}},
	year	 = {2016},
	editor	 = {Karlheinz Schwarz},
	publisher	 = {MDPI},
	journal	 = {Computation},
	series	 = {4(4)},
	pages	 = {19},
	issn	 = {2079-3197},
	doi	 = {http://dx.doi.org/10.3390/computation4040038},
	abstract	 = {We present an Anderson acceleration-based approach to spatially couple
      three-dimensional Lattice Boltzmann and Navier-Stokes (LBNS) flow simulations. This allows to
      locally exploit the computational features of both fluid flow solver approaches to the fullest
      extent and yields enhanced control to match the LB and NS degrees of freedom within the LBNS
      overlap layer. Designed for parallel Schwarz coupling, the Anderson acceleration allows for
      the simultaneous execution of both Lattice Boltzmann and Navier-Stokes solver. We detail our
      coupling methodology, validate it, and study convergence and accuracy of the Anderson
      accelerated coupling, considering three steady-state scenarios: plane channel flow, flow
      around a sphere and channel flow across a porous structure. We find that the Anderson
      accelerated coupling yields a speed-up (in terms of iteration steps) of up to 40\% in the
      considered scenarios, compared to strictly sequential Schwarz coupling.},
}