Unconditionally Stable Calculation of Transonic Potential Flow Through Cascades Using an Adaptive Mesh for Shock Capture

Abstract

This paper describes an unconditionally stable procedure for calculating practical transonic potential flows through two-dimensional cascades. The full potential equation is cast in conservation form and approximated in physical space with centered control area techniques. Discrete analogs of nonphysical weak solutions are eliminated by the introduction of artificial viscosity in supersonic regions using artificial compressibility in which the density is evaluated a certain distance upstream from where it is to be applied. An explicit treatment of the density causes standard iterative procedures to diverge, except on relatively coarse meshes on which shocks are poorly captured. Instead, the insight of a model problem analysis is used to treat the density partially and implicitly.