Abstract
A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhatnagar P., Gross E. and Krook M., 1954, “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems,”Physical Review, Vol. 94, pp. 511–525.
Chen H., Chen S. and Matthaeus W., 1992, “Recovery of the Navier-Stokes Equations Using a Lattice Gas Boltzmann Method,”Physical Review A, Vol. 45, pp. R5339-R5342.
Chen S., Martinez D. and Mei R., 1996, “On Boundary Conditions in Lattice Boltzmann Methods,”Physics of Fluids, Vol. 8, pp. 2527–2536.
Frisch U., Hasslacher B. and Pomeau Y., 1986, “Lattice-Gas Automata for the Navier-Stokes equation,”Physical Review Letters, Vol. 56, pp. 1505–1512.
Inamuro T., Yoshino M. and Ogino F., 1995, “A Non-slip Boundary Condition for Lattice Boltzmann Simuation,”Physics of Fluids, Vol. 7, pp. 2928–2930.
Maier R. S., Bernard R. S. and Grunau D. W., 1996, “Boundary Conditions for the Lattice Boltzmann Method,”Physics of Fluids, Vol. 8, pp. 1788–1801.
McNamara G. R. and Zanetti G., 1988, “Use of the Boltzmann Equation to Simulate Lattice-Gas Automata,”Physical Review Letters, Vol. 61, pp. 2332–2335.
Noble D. R., Chen S., Georgiadis J. and Buckius R. O., 1995, “A Consistent Hydrodynamic Boundary Condition for the Lattice Boltzmann Method,”Physics of Fluids, Vol. 7, pp. 203–209.
Qian Y. H., d’Humieres D. and Lallemand P., 1992, “Lattice BGK Models for Navier-Stokes Equation,”Europhysics Letters, Vol. 17, pp. 479–484.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, I.C. Second order bounce back boundary condition for the latice Boltzmann fluid simulation. KSME International Journal 14, 84–92 (2000). https://doi.org/10.1007/BF03184774
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF03184774