Investigation of the Internal Structure of Shock Profiles for ENO Methods

Solution to systems of hyperbolic conservation laws may be discontinuous. Example of such systems are the Euler equations and Shallow Water equations. To solve systems of hyperbolic conservation laws, numerical methods which can resolve discontinuities have been developed. One family of such methods is the RK(Runge-Kutta)-ENO(Essentially Non-Oscillatory) shock-capturing scheme. Here we study the modified equation of RK-ENO methods by solving the 1D isen-tropic Euler equations. For fast shocks the numerical orbit in phase plane is a single continuous curve. But for slow shocks it may be discontinuous. The results are compared with numerical orbits by LxF(Lax-Friedrichs) scheme for the modified equation. Undersökning av den interna strukturen hos chockprofiler för ENO-methode