Enhanced parallel computation for time-fractional fluid dynamics: A fast time-stepping method with Newton-Krylov-Schwarz solver

Abstract

This paper presents a sum-of-exponentials domain decomposition method for the numerical simulation of two-dimensional unsteady fluid flow and heat transfer using a time-fractional fluid model. We employ a fast time-stepping approach to discretize the time-fractional derivatives, followed by the application of a parallel Newton-Krylov-Schwarz algorithm to solve the resulting discrete nonlinear system. The numerical experiments demonstrate a superior performance of the fast time-stepping method compared to the traditional L1 scheme, particularly in the context of parallel computation, as it substantially reduces the computational complexity and memory usage. The algorithm exhibits robust performance across a wide range of model parameters and solver settings. Notably, it achieves 60% parallel efficiency with the use of 768 processor cores. This study underscores the efficacy of parallel processing as a potent computational strategy for addressing the challenges in solving time-fractional partial differential equations.