Adaptive grid solution for shock-vortex interaction
A time accurate adaptive grid technique is established and applied to analyse the dynamics of a shock wave passing over a vortex. The components of the technique are a shock capturing technique, a grid movement scheme, and the coupling between them. The shock vortex interaction provides an idealized model for studying certain acoustic problems and problems associated with turbulence amplification from shock waves. From a computational viewpoint, severe solution behavior is tracked with a locally high resolution grid. This is required to accurately capture all the complexities that develop in the shock front and the vortex as they approach each other, merge, and continue.
The emphasis herein is on developing a solution method which has the important capability of readily extending beyond the given shock vortex case to address patterns with further complexity. This same extensibility is not as directly accesible with the shock fitting methods employed in [1,2]. The present study uses a shock capturing method that is not constrained to having only one shock in the domain. Furthermore, the present study uses an adaptive grid method which more accurately resolves the captured shocks and vortices. With adaptive grids, each grid points acts like an internal observer whose purpose is to monitor the solution as it develops; regions are accordingly identified as needing finer resolution and then, in response, grid points are redistributed into the targeted regions. A simple and efficent “predictor corrector” procedure is used to incorporate the adaptive grid movement into a static grid Euler equation solver while maintaining the time accuracy of the solution. The predictor corrector technique gives us the benefits of the dynamic grid without having to deal with the grid speed terms that would arise in the governing equations.
KeywordsShock Wave Shock Front Vortex Core Adaptive Grid Planar Shock Wave
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