Discrete Artificial Boundary Conditions for the Lattice Boltzmann Method in 2D

Abstract

Abstract. To confine a spatial domain to a smaller computational domain, one needs artificial boundaries. This work considers the lattice Boltzmann method and deals with boundary conditions for these open boundaries. Ideally, such a condition does not interact with the fluid at all. We present novel two-dimensional discrete artificial boundary conditions to pursue that goal and we discuss four different versions. This type of condition is formulated on the discrete lattice Boltzmann level and does not require a PDE formulation of the fluid. We set a special focus on the D2Q9 model. Our numerical results compare the novel discrete artificial boundary conditions to simulations using the existing non-reflecting characteristic boundary condition and an exit boundary condition.

A Characteristic Boundary Condition for Multispeed Lattice Boltzmann Methods

“…The amplitude variations of incoming waves can be modeled in several ways: They may be i) set to zero to pose a perfectly non-reflecting BC, ii) computed from an imposed macroscopic value or iii) computed from a relaxation towards such a desired value [29]. We refer to [30] and references therein for more details. Here, we stick to annihilating incoming waves by setting their amplitude variations to zero, i.e., we substitute L x with Lx,i = L x,i , outgoing wave, 0, incoming wave.…”

“…This type of setup is commonly modeled by employing a class of BC going under the name of Non-Reflecting BC (NRBC). A few examples are given by i) the perfectly matched layer technique [18], where a damping layer is attached to the computational domain, ii) the discrete artificial boundary condition [19], where the information entering the computational domain is approximated using another LBM simulation and iii) characteristic boundary conditions, where wave amplitude variations are manipulated (e.g. [20]).…”