Shock-Capturing Exponential Multigrid Methods for Steady Compressible Flows

In this paper, a robust and efficient exponential multigrid framework is proposed for computing steady compressible flows. The algorithm based on a global coupling, exponential time integration scheme can provide 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. The resultant exponential multigrid framework is shown to be effective for smooth flows and can stabilize shock-capturing computations without limiting or adding artificial dissipation for medium-strength shock waves.