Asymptotics of a discrete-discontinuity profile in the computation of shock waves by difference schemes
Abstract
The paper examines a class of monotonic difference schemes represented in a conservative form and approximating a quasi-linear hyperbolic differential equation. Necessary and sufficient conditions are formulated under which the numerical solution obtained in shock-wave computation converges in a strong norm at t approaching infinity to a certain limit function. This latter function is monotonic, and satisfies a nonlinear functional equation and prescribed conditions on +, - infinity. The rate of convergence of the numerical solution to the limit one is estimated.
- Publication:
-
IN: Current problems in mathematical physics and computational mathematics (A86-13676 03-64). Moscow
- Pub Date:
- 1984
- Bibcode:
- 1984cpmp.book...22B
- Keywords:
-
- Asymptotic Methods;
- Computational Fluid Dynamics;
- Discrete Functions;
- Finite Difference Theory;
- Shock Discontinuity;
- Shock Waves;
- Convergence;
- Difference Equations;
- Hyperbolic Differential Equations;
- Limits (Mathematics);
- Monotone Functions;
- Fluid Mechanics and Heat Transfer