Mass-flux-based outlet boundary conditions for the lattice Boltzmann method

We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is further demonstrated with numerical experiments.

[1]  M. Olshanskii,et al.  On simulation of outflow boundary conditions in finite difference calculations for incompressible fluid , 2000 .

[2]  S. Wolfram.  Cellular automaton fluids 1: Basic theory , 1986 .

[3]  J. Hyväluoma,et al.  A boundary condition for arbitrary shaped inlets in lattice–Boltzmann simulations , 2009 .

[4]  G. Karniadakis,et al.  Outflow Boundary Conditions for Arterial Networks with Multiple Outlets , 2008, Annals of Biomedical Engineering.

[5]  Skordos,et al.  Initial and boundary conditions for the lattice Boltzmann method. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  D. Martínez,et al.  On boundary conditions in lattice Boltzmann methods , 1996 .

[7]  Pierre Lallemand,et al.  Consistent initial conditions for lattice Boltzmann simulations , 2006 .

[8]  Orestis Malaspinas,et al.  Straight velocity boundaries in the lattice Boltzmann method. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  J. Bérenger.  Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves , 1996 .

[10]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[11]  Paul Lavallée,et al.  Boundaries in lattice gas flows , 1991 .

[12]  Dominique d'Humières,et al.  Multireflection boundary conditions for lattice Boltzmann models. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Lars Davidson,et al.  Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition , 1998 .

[14]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[15]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[16]  I. Karlin,et al.  Grad's approximation for missing data in lattice Boltzmann simulations , 2006 .

[17]  Robert S. Bernard,et al.  Boundary conditions for the lattice Boltzmann method , 1996 .

[18]  W. Shyy,et al.  Improved treatment of the open boundary in the method of Lattice Boltzmann equation , 2005 .

[19]  Zhaoxia Yang,et al.  Outflow boundary conditions for the lattice Boltzmann method , 2008 .

[20]  G E Karniadakis,et al.  LARGE‐SCALE SIMULATION OF THE HUMAN ARTERIAL TREE , 2009, Clinical and experimental pharmacology & physiology.