Real-world problems encountered in Computational Fluid Dynamics (CFD) are often governed by complex systems of parametrized partial differential equations. The resolution of such problems requires the employment of advanced numerical tools for simulation purposes. Classic numerical simulations, which aim to accurately replicate experimental data, may require thousands or even millions of degrees of freedom, resulting in time and memory-intensive processes. Reduced Order Models (ROMs) constitute a class of well-established techniques aimed to accelerate such high-fidelity simulations in a large variety of fields by reducing the complexity of the model. Here we present an overview of ROMs in the field of CFD with a special focus on approaches based on the Proper Orthogonal Decomposition (POD) technique. The paper also resumes the most remarkable recent advances of ROMs in industrial, biomedical, and environmental applications.
