New diagonal implicit scheme for the compressible Navier-Stokes equations

The present study is concerned with a new implicit scheme for solving the Navier-Stokes equations for a compressible fluid. A viscous splitting algorithm is used to decouple the convection and diffusion parts of the equations. A new two-point difference scheme, which is an extension of the MacCormac implicit scheme, is adopted for the convective part. The Crank-Nicolson scheme is employed for the diffusion part. Attention is given to aspects of algorithm development, numerical experiments in one-dimensional space, an algorithm in two-dimensional space, and the shock-wave boundary-layer interaction problem.