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By Simon McBeath
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Extra info for Aerodinámica del automóvil de competición
Otherwise, it is certain that gradient-based methods will follow the gradient information near other local optimal points and converge to those values. Increasing the number of initial datasets eventually leads to the BFGS method finding the global optimal solution, but such treatment is very inefficient. Real world engineering optimization problems, such as IC engine optimization, are normally much more complicated than these two problems. Furthermore, the problems are most likely not differentiable and the number of local optimal solutions can also be large, which renders the application of gradient-based methods inefficient or impractical for such engineering problems.
For the first problem, since it has only one local and global optimal solution, the BFGS method started with a single random set of the two input parameters. 1 Optimization Algorithms 17 Fig. 2 Multiple peak values problem Fig. 3 Function value of the one-peak problem using BFGS method optimal solution of unity with only 31 evaluations, which is quite efficient, as expected. Technically, one can also start the BFGS method with a single set of input variables for the second problem. However, it is almost impossible to obtain the global optimal solution with such configuration as it is easy to see that the method has a very high chance of converging towards a local (non) optimal point.
It takes the dispersed phase as a continuous fluid and introduces several continuous scalar fields to represent the dispersed phase. 2 Engine Modeling with Computational Fluid Dynamics 31 both phases. Therefore, the dispersed phase is modeled at the macroscopic level with this approach. This method leads to significant difficulties in modeling complex phenomena such as droplet breakup, droplet interaction, and droplet evaporation, which are essential in IC engine applications. It is also very difficult to establish the representation of the turbulent stresses and transport in the liquid phase.