Concluding Remarks

Summary

The objective of this book was to present, in a more or less coherent manner, a class of shock-capturing numerical methods for solving hyperbolic problems. The methodology has been presented via simple model equations. For non-linear systems we have chosen the time-dependent compressible Euler equations as the representative sytem of hyperbolic conservations laws. Our original intention was to include the application of the methods to three other systems of practical interest, namely the steady supersonic Euler equations, the shallow water equations and the artificial compressibility equations associated with the incompressible Navier-Stokes equations, but we ran out of space.