Thesis for degree: Licentiate of Engineering

Figure 2.6: Effective boundary arrangement for the coupling of FVM and LBM.
The FV model is formulated with adimensionless system and so LBM should also be
converted to a dimensionless system to meet this constraint. The approach to connect the FV
model and LB model at the boundary is by linear interpolation because the variables are not
defined at the same positions in the domain. This gives the following relationships for the
velocity.
(2.34)
(2.35)
(2.36)
(2.37)
The procedure would start off, for the inner nodes, so that the incoming particle distribution
function f a at time t is used to compute the local density ρ and velocity u or v. For the
boundary nodes all three variables are obtained from the variables of the FV model at time t
[26, 28]. Next, all nodes are subject to the collision step. Finally, the inner nodes will perform
the streaming step.
2.4 Previous case studies of SOFCs in LBM
Although LBM is a relatively new actor among the numerical modeling methods, some work
has already been carried out on SOFCs. There are some limitations connected to the LBM
that need to be highlighted. These have been detected through previous studies. LBM has
only recently been used as a numerical method for transport processes in SOFC and compared
with conventional methods such as FDM, FEM and FVM [24]. According to Joshi et al., there
is still a need for a supercomputer to perform the LBM simulations. The method is described
in detail by Joshi et al. [14-16, 23] and a comprehensive discussion of the method and various
terms in the LB equation are offered. Hence, the reader is referred to the work of Joshi et al.
for further discussion.
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