Advanced Finite Element Methods for Solving Fluid Dynamics Problems in Engineering Applications

In this research, Advanced Finite Element Methods (FEM) for engineering applications’ fluid dynamics problem solving are investigated, where high order discretization, hybrid solvers and AI enhanced FEM models are studied. SUPG, VMS and DG methods were analyzed in terms of their accuracy and efficiency of computation. We calculated about 35% reduction in numerical diffusion using SUPG vis a vis conventional FEM carried out at Reynolds numbers Re = 10⁵ to 10⁷. Turbulence modeling accuracy was enhanced by 28% with VMS approach, whereas 42% increased shock capturing capability have been realized with DG-FEM. Moreover, the computational time was reduced to 50% by integrating physics informed neural networks (PINNs) at a 97% accuracy level. The research also validated hybrid mesh free FEM approaches that allow 15% higher efficiency in fluid structure interaction problems. The fact that we can implement these findings in the context of real time engineering applications using AI enhanced FEM techniques indicates that these are strong candidates. Finally, the study shows that the advanced FEM methods are more accurate, more stable and far more computationally efficient than traditional models. FEM solvers accelerated by GPU and adaptive meshing strategies should be explored in future research for further optimality.