A cell-vertex upwind scheme for two-dimensional supersonic Euler flows

An implicit cell-vertex upwind method is presented for the solution of the two-dimensional Euler equations for supersonic flows. It is based on the two-point difference scheme introduced by S.F. Wornom, but contains many significant developments. Particular attention is given to the implementation of boundary conditions, to ensure that no ''numerical'' boundary conditions are required, and ''image'' cells are avoided, making the scheme ideal for use in conjunction with a multiblock approach. Examples are given for quasi-one-dimensional nozzle flows, and in two dimensions, oblique shock reflection, a shock interaction problem, and a supersonic intake problem. The accuracy and efficiency of the scheme is demonstrated, along with its ease of use.