Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence subsonic). We proved that such a transonic characteristic discontinuity is structurally stable under small perturbations of the upstream supersonic flow in $BV$. The existence of a weak entropy solution and Lipschitz continuous free boundary (i.e. characteristic discontinuity) is established. To achieve this, the problem is formulated as a free boundary problem for a nonstrictly hyperbolic system of conservation laws; and the free boundary problem is then solved by analyzing nonlinear wave interactions and employing the front tracking method.Comment: 26 pages, 3 figure

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

Institute for Computational Mechanics in Propulsion (ICOMP) fourth annual review, 1989

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated jointly by Case Western Reserve University and the NASA Lewis Research Center. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1989 are described

Subsonic flows with a contact discontinuity in a two-dimensional finitely long curved nozzle

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a two-dimensional finitely long slightly curved nozzle. We establish the existence and uniqueness of subsonic flows with a contact discontinuity by prescribing the entropy function, the Bernoulli quantity and the horizontal mass flux distribution at the entrance and the flow angle at the exit. The problem can be formulated as a free boundary problem for the hyperbolic-elliptic coupled system. To deal with the free boundary value problem, the Lagrangian transformation is employed to straighten the contact discontinuity. The Euler system is reduced to a nonlinear second-order equation for the stream function. Inspired by \cite{CXZ22}, we use the implicit function theorem to locate the contact discontinuity. We also need to develop an iteration scheme to solve a nonlinear elliptic boundary value problem with nonlinear boundary conditions in a weighted H\"{o}lder space