The stability of multi-dimensional shock fronts
Abstract
The linearized stability of the multidimensional shock-front solutions of the M x M system of hyperbolic conservation laws is investigated analytically. The main theorems for variable coefficients in the linearization of a curved shock front are presented, and the uniform-stability conditions for the equations of compressible flow (the 2D isentropic equations and the 3D Euler equations) are considered. An estimate of the basic variable coefficient is obtained, and the existence and differentiability of the solutions is demonstrated. For cases with several space variables, the stability of the shock-front solutions of a scalar conservation law is shown to be weaker than that of the ideal-gas Euler solutions.
- Publication:
-
NASA STI/Recon Technical Report A
- Pub Date:
- January 1983
- Bibcode:
- 1983STIA...8421308M
- Keywords:
-
- Conservation Laws;
- Flow Stability;
- Flow Theory;
- Hyperbolic Functions;
- Linearization;
- Shock Fronts;
- Boundary Value Problems;
- Compressible Flow;
- Euler Equations Of Motion;
- Existence Theorems;
- Flow Coefficients;
- Flow Equations;
- Gas Dynamics;
- Isentropic Processes;
- Fluid Mechanics and Heat Transfer