This presentation will focus on strategies to optimize numerical simulations in incompressible fluid mechanics, with the aim of reducing computational costs. The central question addressed is how to effectively reuse pre-computed data in new simulations, particularly when the simulation parameters differ from those originally used to generate the data. I will explore both linear and nonlinear interpolation techniques, which allow for the adaptation of pre-calculated solutions to new scenarios. More precisely, the presentation will cover the use of reduced-order models (such as Proper Orthogonal Decomposition, POD) and optimal transport methods to reduce computational complexity while maintaining accuracy. These approaches offer promising solutions for accelerating simulations without compromising on precision, enabling more efficient and scalable computations in fluid dynamics.