The recent developments in the research area of numerical methods for partial differential equations (PDEs) and computational fluid dynamics (CFD) have shown a strong focus on enhancing the accuracy, stability, and efficiency of numerical solvers. There is a notable trend towards the integration of advanced numerical techniques such as exponential integrators, discontinuous Galerkin methods, and mixed finite element methods with innovative approaches like neural operators and multi-objective optimization for automatic solver discovery. These advancements are particularly aimed at addressing complex problems in porous media, traffic flow modeling, and thermo/poro-viscoelasticity, among others. The field is also witnessing a shift towards more robust and adaptive methods capable of handling uncertainties and transient faults in high-performance computing environments. Additionally, there is a growing interest in the development of parallel-in-time methods and efficient preconditioning techniques to tackle large-scale problems. Notably, the integration of machine learning with traditional numerical methods is emerging as a promising direction for optimizing solver performance and adaptability.

Noteworthy Papers:

• The integration of neural operators with iterative solvers for automatic discovery of optimal meta-solvers.
• The development of a second-generation convexification method for solving coefficient inverse problems in epidemiology.
• The proposal of a novel traffic flow model based on the urban-porous city concept, integrating non-stationary convection-diffusion-reaction PDEs with Darcy-Brinkman-Forchheimer systems.