Optimization and Computational Fluid Dynamics - Department of ...

54 Gábor Janiga
Error for Re∗
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Wilcox (1998)
Re∗ = 395 Re∗ = 590 Re∗ = 950 Re∗ = 2000
Fig. 2.24 The four objectives of the optimization represented using parallel coordinates
for the individuals belonging to the POF
Table 2.6 Parameters of the EA for the turbulence model optimization (Case C)
Parameter Value
Population size, N 100
Generations 100
Survival probability 50%
Average probability 30%
Crossover probability 20%
Mutation probability 100%
Mutation magnitude 50% a (i.e., ±25%)
a This value is multiplied by 0.95 at each generation. For example, the mutation magnitude
is 31.5% (±1.75%) after 10 generations or 0.3% (±0.15%) after 100 generations. Mutation
magnitude must be decreased during the optimization process to stabilize the population.
using eight parameters. This is a simple description that could be refined.
Computing times can be further reduced by using parallelization, as demonstrated
in this chapter. More complex, practical industrial cases are solvable
using on one side appropriate modeling and simplification of the problem and
on the other side parallelization.
Furthermore, we have demonstrated that optimization of complex flows
involving heat transfer and complex chemical reactions is possible, provided
very efficient numerical methods are used for the optimization process (here,