The field of numerical methods for complex fluid dynamics is experiencing significant advancements, driven by the development of innovative techniques for solving partial differential equations. A key trend is the integration of machine learning and physics-based methods, such as neural networks and discontinuous Galerkin methods, to improve the accuracy and efficiency of simulations. Another area of focus is the development of structure-preserving variational schemes, which can capture the complex dynamics of systems with moving boundaries and nonlinear interactions. These advances have the potential to significantly impact various fields, including materials science, chemistry, and biology. Noteworthy papers include: A Hybridizable Discontinuous Galerkin Method for the Miscible Displacement Problem Under Minimal Regularity, which establishes convergence of a numerical method under low regularity assumptions. Primal-dual splitting methods for phase-field surfactant model with moving contact lines, which proposes a novel scheme for simulating complex droplet dynamics with surfactants.