On the spectral viscosity method in multidomain Chebyshev discretizations

This paper describes how one can use the spectral vanishing viscosity method pro posed by Tadmor in multidomain solution of hyperbolic systems Interface conditions are derived using a variational approach and open boundary conditions are derived using the approach used in for incomplete parabolic systems Introduction Filtering of the solution is a very common technique when using spectral methods on problems with solutions of limited regularity The main reason for using ltering is to prevent the buildup of large components of high spatial frequency and hence to stabilize the solution There are many variants of ltering described in the literature see e g for techniques to handle discontinuities and for a general overview We will here concentrate on problems where we don t have to deal explicitly with shocks or discontinuities but where we lter to stabilize the smooth solution We consider a quasi linear hyperbolic system