Efficient Solvers for Nonlinear Partial Differential Equations in Computational Fluid Dynamics

Abstract

Improving the computational efficiency of solving nonlinear partial differential equations (PDEs) is a key area of focus for this research, which has the ability to significantly impact computational fluid dynamics (CFD) simulations. The complexities of fluid flow phenomena can be difficult for traditional methods to handle, leading to simulations that are resource-intensive and computationally slow. The urgent requirement for improved computational tools capable of quickly and precisely simulating complex fluid dynamics scenarios is the driving force behind the significance of this research. New approaches are needed to solve nonlinear partial differential equations (PDEs) in computational fluid dynamics (CFD), which are characterized by turbulent flows, fluid-structure interactions, and high computing resource intensity. Adaptive mesh optimization and high-performance computing architectures are combined in the AMO-HPI technique, which provides a strategic solution. Adaptive Mesh Optimization based on High-Performance Integration (AMO-HPI) is suggested in this research as a way to improve the accuracy of solutions by focusing computational resources on regions of interest through adaptive mesh refinement and coarsening. Making effective use of shared-memory parallelism and message-passing interfaces (MPI) to divide up computational tasks. Improvements in engineering system performance, reliability, and safety can be achieved by the effective simulation of fluid dynamics processes, which opens up new design areas that were previously unreachable. When compared to other methods, AMO-HPI performs better in simulations due to its optimal resource utilization and decreased processing time. In addition to improving CFD methodology, this research could have far-reaching effects on engineering design processes in several industries, which would be great for innovation and sustainable development.