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2.3 Computational Fluid Flow Simulation on Body Fitted Mesh Geometry
with IBM Cell Broadband Engine and FPGA Architecture 57
the dissipative stabilization term. A finite volume scheme is characterized by the
evaluation of F N , which is the function of both U L and U R . Applying the simple
and robust Lax-Friedrichs numerical flux function defined as
F N = F L + F R
2
− (|ū| + ¯c) U R − U L
. (2.10)
2
In the last equation c is the local speed of sound, F L =F x (U L ), F R =F x (U R ) and
bar labels speeds computed at the following averaged state
Ū = U L + U R
. (2.11)
2
The last step concludes the spatial discretization. Finally, the temporal derivative
is dicretized by the first-order forward Euler method:
dU i,j
dt
= U n+1
i,j − Ui,j
n
∆t
, (2.12)
where U n i,j is the known value of the state vector at time instant n, U n+1
i,j
the
unknown value of the state vector at time instant n + 1, and ∆t the time step.
By working out the algebra described so far, leads to the following discrete form