Exponential Time Differencing Gauge Method for Incompressible Viscous Flows (Communications in Computational Physics, 2018)
In this paper, we study an exponential time differencing method for solvingthe gauge system of incompressible viscous flows governed by Stokes or Navier-Stokesequations. The momentum equation is decoupled from the kinematic equation at adiscrete level and is then solved by exponential time stepping multistep schemes inour approach. We analyze the stability of the proposed method and rigorously provethat the first order exponential time differencing scheme is unconditionally stable forthe Stokes problem. We also present a compact representation of the algorithm forproblems on rectangular domains, which makes FFT-based solvers available for theresulting fully discretized system. Various numerical experiments in two and threedimensional spaces are carried out to demonstrate the accuracy and stability of theproposed method.