AN EFFECTIVE TREATMENT OF NUMERICAL SHOCKWAVE INSTABILITIES WITH RESIDUAL DISTRIBUTION SCHEMES: APPLICATION TO HYPERSONIC FLOWS AROUND BLUNT BODIES.

摘要

In the present contribution the issue of simulating hypersonic flows by means of Residual Distribution Schemesrnis discussed. In particular, this discretization techniquernis briefly presented and its current capabilities reviewed.rnCertain aspects of the technique needing some adjustmentsrnto deal with the distinctive characteristics of thernhypersonic regime are identified. Among them, extensivernattention is given to the subject of the carbuncle phenomenon, a critical numerical instability preventing thernaccurate simulation of hypersonic flows around bluntedrnconfigurations. After reviewing the known remedies forrnthis instability, the single one known to be usable in thernResidual Distribution context is presented and studied inrndepth. A sensitivity analysis with respect to its singlerncontrolling parameter is performed. The fix effectivity inrnavoiding the carbuncle is proven. A simple technique torncure an, as far as we know, previously unreported lack ofrnconvergence is presented. The importance of a consistentrntreatment of energy dissipation is assessed, and as a result a complete family of carbuncle fixes is derived. Finally, the numerical treatment is validated for the flow around a cylinder in hypersonic conditions.