Domain decomposition and model integration - Computational River Dynamics - page 329

Figure 8.6 Treatment of pressure-correction at the interface.

Solution procedure
After the governing equations are discretized in a multiblock domain, the algebraic
equations on each block can be solved in the same way as for a single block prob-
lem. However, an additional level of iteration among grid blocks must be introduced.
Two different iteration strategies can be established. The first strategy is to form
an outer loop for the iteration among blocks and an inner loop for the iteration
among equations. In the outer loop, information on all relevant variables is trans-
ferred. Denoting the total number of blocks as nb , the procedure of the multiblock
SIMPLE algorithm at each time step is:

for blocks 1 to n b

(1) Guess the pressure field p ∗ ;
(2) Solve the momentum equations to obtain U x and U y ;
(3) Solve the pressure-correction equation to obtain p ;
(4) Calculate p n + 1 , U n + 1

x , and U n + y ;
(5) Treat the corrected pressure p n + 1 as a new guessed pressure p ∗ , and repeat the
procedure from step 2 to step 6 until a converged solution is obtained;
(6) Conduct the calculation of sediment transport and bed change, if needed.

end for

The second strategy forms an outer loop for the iteration among equations and an
inner loop among blocks. In the inner loop, information on all relevant variables is
transferred. The corresponding procedure for the multiblock SIMPLE algorithm at
each time step is:

(1) Guess the pressure field p ∗ , for blocks 1 to nb ;
(2) Solve the momentum equations to obtain U x and U y , for blocks 1 to nb ;