Carbuncle Phenomena and Other Shock Anomalies in Three Dimensions

Keiichi Kitamura * and Eiji Shima † Japan Aerospace Exploration Agency (JAXA), Sagamihara, Kanagawa, 252-5210, Japan and Philip L. Roe ‡ University of Michigan, Ann Arbor, MI 48109, USA Hypersonic flow computations have proved to be very troublesome due to the appearance of shock anomalies (instabilities and oscillations), such as carbuncle phenomenon. These anomalies are categorized into one-dimensional (1D) and multidimensional (MD) modes, and these modes both arise from many factors and their combinations. Accurate prediction of hypersonic heating, a key issue in hypersonic flow computations, is therefore challenging especially for three dimensions (3D). In the present study, we focus on 3D shock anomalies and heating motivated by the following reasons: 1) Intuitively, MD shock anomalies are considered to develop more likely in 3D than in two dimensions (2D), but it cannot be proved mathematically, nor has it been numerically demonstrated; specifically, it is not clear yet whether the third dimension plays another role which is absent in 2D. 2) Most of proposed remedies for MD anomalies had been tested in 1D or 2D setups in the literature, but it is not guaranteed whether such MD dissipations actually work well in 3D. 3) It is already known to be troublesome to extend some of MD methods developed in 2D considerations to 3D. The numerical results show that 3D anomalies are too complicated to be predicted from their 2D counterparts, and that they can either be partly removed or (even worse) enhanced by MD dissipations. Therefore, robustness of a numerical method which worked well in 2D may not be preserved in 3D.