Shock wave instability and the carbuncle phenomenon: same intrinsic origin?

The theoretical linear stability of a shock wave moving in an unlimited hom ogeneous environment has been widely studied during the last fifty years. I mportant results have been obtained by Dyakov (1954), Landau & Lifchitz (19 59) and then by Swan & Fowles (1975) where the fluctuating quantities are w ritten as normal modes. More recently, numerical studies on upwind finite d ifference schemes have shown some instabilities in the case of the motion o f an inviscid perfect gas in a rectangular channel. The purpose of this pap er is first to specify a mathematical formulation for the eigenmodes and to exhibit a new mode which was not found by the previous stability analysis of shock waves. Then, this mode is confirmed by numerical simulations which may lead to a new understanding of the so-called carbuncle phenomenon.