A class of central bidiagonal schemes with implicit boundary conditions for the solution of Euler's equations

A class of implicit bidiagonal schemes is developed for the conservative Euler equations. The schemes are based on a predictor corrector approach for the characteristic variables, adapted according to the sign of the characteristic speeds of information. They are second order accurate in space and time, and have intrinsic dissipative properties. A new fully implicit boundary treatment is developed for this class of schemes, allowing high CFL numbers in all regions of the flow domain. A simple post processing technique is used to obtain high accuracy in the shock regions. Results are presented for the quasi-one-dimensional flow in a nozzle.