4D flow MRI is a promising tool in cardiovascular imaging. However, its lack of resolution can degrade some biomarkers' evaluation accuracy. The computational fluid dynamics (CFD) simulation is considered as the reference method to improve numerically the image resolution. However, CFD simulations are complex and time consuming, and matching their results with 4D Flow MRI data is very challenging. This paper aims to introduce a fast and efficient super-resolution (SR) approach thanks to the minimization of a L 2-penalized criterion, which combines a weighted least-squares data fidelity term and Navier-Stokes equations. The algorithm has been validated on synthetic and phantom datasets and compared to state-of-the-art solutions. Moreover, a prospective study is conducted on the segmentationfree application of the proposed algorithm.