Efficient Steady Flow Computations with Exponential Multigrid Methods

Abstract

An exponential multigrid framework is developed and assessed with a modal high-order discontinuous Galerkin method in space. The algorithm 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.