1 A Possible Mechanism for the Appearance of the Carbuncle Phenomenon in Aerodynamic Simulations Marcus V. C. Ramalho 1 Universidade de Brasília, Brasília, DF, 70919-970, Brazil and João Luiz F. Azevedo 2 Instituto de Aeronáutica e Espaço, São José dos Campos, SP, 12228-903, Brazil The paper discusses a possible mechanism for the appearance of the carbuncle phenomenon in the numerical computation of supersonic flows. The hypothesis here explored considers that such mechanism may involve the interaction between shock waves and density inhomogeneities created within the nonphysical structure of the numerical shocks. The present proposal seems to be supported by two-dimensional results of the numerical simulation of steady flows around a blunt body and of the unsteady propagation of a plane shock. I. Introduction It has been known for nearly 20 years that some shock-capturing methods can generate spurious solutions when applied to seemingly simple problems such as the calculation of the flowfield containing a detached shock wave ahead of a blunt body in supersonic flow. The so-called carbuncle phenomenon, first reported by Peery and Imlay 1 , was initially associated with the use of Roe’s approximate Riemann solver in the spatial discretization of the convective terms in the Euler equations. However, it was later found to affect several other methods. In its most typical form, the carbuncle phenomenon consists of a protrusion ahead of the shock, which contains a region of circulating and possibly stagnated flow (see Fig. 1). The overall flowfield appears to satisfy the Euler equations, at least in a weak sense and in its discretized form, since solutions including the carbuncle satisfy usual convergence tests. The phenomenon was later observed by several authors, and a fairly extensive literature on its possible causes and cures was subsequently developed. 2-9 It has been found that the carbuncle appears to occur only with shock-capturing schemes that are designed to preserve contact discontinuities. 3 One explanation is that such schemes provide insufficient dissipation in the shock region, particularly in the direction parallel to the shock, 2, 3, 12 thereby suffering from instabilities that may result in the formation of the carbuncle. Dumbser et al. 4 analyzed the linear stability of several discretization schemes and concluded that those which are more carbuncle-prone are also likely to be inherently unstable under certain conditions. Quirk 2 observed that, although adding dissipation in the direction parallel to the shock was a common method to suppress the carbuncle in contact discontinuity-preserving schemes, there were no physical or numerical grounds for resorting to such a “cure”. It was simply a convenient means to get rid of the problem. A different type of explanation was attempted by Robinet et al., 5 who suggested that the origin of the carbuncle could lie in the physical instability of the surface of discontinuity itself, i.e., the shock wave. According to earlier research on the problem of shock wave stability (see, for example, Ref. 10), the plane shock wave formed in a polytropic gas is always stable. Robinet et al., 5 nevertheless, reported to have found a mode which could give rise to instability and that had been overlooked by previous researchers. Moreover, the characteristics of this mode seemed to agree with observations that had been made in connection with the carbuncle phenomenon. This discovery, however, was later contested by Coulombel et al., 11 who reaffirmed that a plane shock wave in a polytropic gas could not, in fact, be physically unstable, and showed that the derivation of Robinet et al. 5 was incorrect in some respects. 1 Graduate Student, Instituto de Física, Caixa Postal 04455; E-mail: mvcramalho@gmail.com. AIAA Member. 2 Senior Research Engineer, Aerodynamics Division, Departamento de Ciência e Tecnologia Aeroespacial; E-mail: azevedo@iae.cta.br. Associate Fellow AIAA. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando, Florida AIAA 2010-872 Copyright © 2010 by M.V.C. Ramalho and J.L.F. Azevedo. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.