efficient parallel computation to simulate blood flow - CiteSeerX

The NS equations simplify then into the Stokes equation in the neighborhood of
the inlet and outlet of the fluid domain Ω f . To avoid reflection of acoustic waves at
the outlet one may then use transparent boundary conditions [19].
On the horizontal wall we assume either the periodicity of all variables, or we
impose the flow speed to be U w .
Further improvement in the grid discretization implementation may use a high
order interpolation scheme for the convective term that introduces less dissipation
and a mesh refinement in the neighborhood of the interface Sw.
f
We have all the information to solve the NS equations. The main goal of this
project is to get the fastest results. A short computation time to obtain a solution
of the NS equation requires an efficient solver.
3.3 Aitken Schwarz 3D
For solving the linear system, our solver uses also the Aitken-Schwarz Domain decomposition
technique presented in Chapter 2 for a two dimensional case. The main
difference between the two and three dimensional simulation is that the Fourier decomposition
and the subdomain solver solve only a tridiagonal problem.
The domain Ω = (0, Lx) × (0, Ly) × (0, Lz) is decomposed into q overlapping
strips Ω i = (X i l , Xi r ) × (0, Ly) × (0, Lz) with X2 l < X 1 r < X3 l < X 2 r , ..., Xq l
< X q−1
r
as
described in Figure 3.4
The pressure unknown is developed into the sine expansion into the physical space
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