Thesis for degree: Licentiate of Engineering

lies to correctly set up the interface conditions and also to manage the conversion from the
lattice to the macroscopic variables or vice versa [28].
The positioning of the variables for the LB model and FV model is presented in Figure 2.5.
The FV model uses a staggered grid where the scheme is explicit for the velocity and implicit
for the pressure [25]. The choice of a staggered grid for the FV model is to prevent possible
pressure oscillation. The LB variables are evaluated at the corner positions for all lattice
variables at the same positions. For the FVM, the velocity variable is evaluated at the
interface of the grid cells between two corner positions and the pressure is evaluated at the
center of the grid cell [26]. Note that only a 2D domain is discussed here.
Figure 2.5: The indexes and grid positions for the LB and FV models variables.
This leads to the question of how to couple the two models at their interacting boundary. The
set of boundary nodes for the two models are connected by an overlap layer of nodes so linear
interpolation can be performed to find the effective boundary condition [26]. This overlap is
illustrated in Figure 2.6. Note that the overlap for the interface is about one and a half grid
cell to capture the physical processes at the boundary. This can be chosen arbitrarily
depending on the specific need of detailed information and high resolution, and the access to
computational power.
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