Preconditioning compressible flow calculations on stretched meshes

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 improves full coarsening multigrid performance by clustering high frequency components of the spatial Fourier footprint away from the origin for effective damping by a Runge-Kutta time stepping scheme. For viscous computations on highly stretched meshes, a J-coarsening multigrid algorithm is adopted that provides adequate clustering of all modes inside the boundary layer. In contrast to previous approaches, the methods presented are robust when used in conjunction with high resolution schemes on fine meshes and with multigrid. Substantial speed-ups are demonstrated for a variety of Euler and laminar and turbulent Navier-Stokes test cases.