Preconditioning on stretched meshes

Abstract

High aspect ratio cells in a computational mesh compound the inherent stiffness in the Euler and Navier-Stokes equations which arises from a disparity in the propagative speeds of convective and acoustic modes. A mesh-aligned preconditioning strategy is examined which is intended to improve multigrid performance in two ways: a) enhancing propagation of disturbances by shaping wave front envelopes to match cell aspect ratios, b) clustering high frequency components of the spatial Fourier footprint away from the origin for effective damping by an optimized Runge-Kutta time stepping scheme. In contrast to previous approaches, the method is robust when used in conjunction with high resolution schemes on fine meshes and with multigrid. Results are provided for a number of standard airfoil test cases.