The recent developments in the research area of computational fluid dynamics and numerical methods for partial differential equations (PDEs) indicate a strong trend towards enhancing the efficiency, accuracy, and robustness of numerical solvers. There is a notable focus on developing preconditioners and multigrid methods to improve the scalability and convergence of high-order discretizations, particularly for problems involving complex geometries and high-contrast media. Additionally, there is a growing interest in integrating machine learning techniques with traditional CFD methods to accelerate simulations and handle large datasets more effectively. The field is also witnessing advancements in the development of adaptive and hybrid methods that combine the strengths of different numerical approaches, such as combining semi-Lagrangian methods with low-rank approximations to tackle high-dimensional problems. Furthermore, there is a significant push towards ensuring numerical stability and conservation properties in the solutions of PDEs, with innovative methods like the weighted scalar auxiliary variable (SAV) approach being proposed to bridge the gap between energy stability and computational efficiency. Overall, the research is moving towards more sophisticated and integrated approaches that aim to address the computational challenges posed by complex fluid dynamics and PDEs.