Fast algorithm for function minimization

Question

Hello I would like to optimize (in my case find the minimum of) a function efficiently. If R is the set of real numbers, then my function goes from R^n to R, so it is a real-valued function with n real variables. In my case n is between 2 and 10 (but usually its gonna be 4 or 5.

I found many optimization algorithms, but in my specific case, the function is very costly to evaluate, so some are not tailored, in the sense that they need a great amount of evaluations to be efficient.

In my problem, each evaluation is in fact a CFD simulation that can take up to twenty minutes. Also, I would like this function minimization to occur during (or after) a main optimization process that has a budget of 1000 function evaluations tops.

The minimization process should then not take as much evaluations, and if it occurs during my main optimization, I would like my minimization algorithm to be efficient with a limit of 50 function evaluations for example (or a bit more if needed).

I do not seek to find the global minima at all cost, but at least to minimize my function satisfactorily within a relatively small budget of function evaluations (50 to 100).

Could someone lead me to one of those algorithms, if they ever exist ? Thanks and regards, TOP1.