The field of numerical methods for fluid dynamics and related problems is witnessing significant developments, with a focus on improving the accuracy, efficiency, and robustness of numerical schemes. Researchers are exploring new approaches, such as fully discrete error analysis, multidimensional active flux methods, and positivity-preserving central DG methods, to tackle complex problems in fluid dynamics, magnetohydrodynamics, and stochastic turbulent flow. Noteworthy papers in this area include the proposal of a fully discrete truly multidimensional active flux method for the two-dimensional Euler equations, which guarantees positivity of pressure and density, and the development of a provably positivity-preserving, globally divergence-free central DG method for ideal MHD systems. Another significant contribution is the introduction of a hyperbolic finite difference scheme for anisotropic diffusion equations, which preserves the discrete maximum principle. These innovative methods and techniques are expected to have a significant impact on the field, enabling researchers to simulate and analyze complex fluid dynamics and related phenomena with greater accuracy and efficiency.