neural networks work well for problems having a hierarchical structure and normally you need a lot of training data. However, since you know a lot about the physical properties of your problem, I would use these knowledge and go for finite element methods.
AI is one method can adopt the knowledge from environment inform. IF the problem need read fast from environment and minimize the human interactions, i suggest please use AI. Otherwise, you can use CFD method, if the parameter or variable was known and structured. Why i choose this suggest, because AI worked in semistructured and unstructured problem. In CFD, this method very structure problem.
To my best knowledge, there are three main methods to study fluid dynamics problems, namely experiment analysis, CFD and theory modeling. Until now there are rarely AI-based methods for solving fluid dynamics problems, while CFD or FEM methods are applied extensively in this area.
please note "Artificial neural network, fuzzy logic, optimization methods like genetic algorithm etc." are "Computational Intelligence" methods, which should be seen just as a sub-set of AI