Efficient p-multigrid method based on an exponential time discretization for compressible steady flows

2018/06/30 by Li, Shu-Jie
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1807.01151

Abstract

An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order (p-order polynomial) modal discontinuous Galerkin method. The core algorithm that based on a global coupling, exponential time integration scheme provides strong damping effects to accelerate the convergence towards the steady state, while high-frequency, high-order spatial error modes are smoothed out with a s-stage preconditioned Runge-Kutta method. Numerical studies show that the exponential time integration substantially improves the damping and propagative efficiency of Runge-Kutta time-stepping for use with the p-multigrid method, yielding rapid and p-independent convergences to steady flows in both two and three dimensions.

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