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Report no. 95/10

Preconditioning on Stretched Meshes

Niles A. Pierce Michael B. Giles
Oxford University Computing Laboratory
Numerical Analysis Group

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.

Key words and phrases: CFD, compressible flow,
preconditioning, stretched meshes

This work was funded by the Rhodes Trust.

Oxford University Computing Laboratory
Numerical Analysis Group
Wolfson Building
Parks Road
Oxford, England OX1 3QD
E-mail: Niles.Pierce@comlab.oxford.ac.uk June, 1995