Multi-dimensional formulation of CSCM - An upwind flux difference eigenvector split method for the compressible Navier-Stokes equations

In studies concerned with the quasi one-dimensional streamtube equations, Lombard et al. (1982) have presented the basis for a new family of implicit finite difference methods for the compressible Euler and Navier-Stokes equations. According to a procedure, termed the Conservative Supra-Characteristics Method (CSCM), difference equations are formed of the pieces from a natural characteristics based eigenvector decomposition of the adjacent two point flux difference for the hyperbolic (convective) terms in any general curvilinear coordinate direction. The present investigation is concerned with a linearized approximately factored implicit algorithm for a more robust and rapidly converging pseudo time-dependent finite difference scheme for the compressible Navier-Stokes equations. The CSCM flux difference split upwind implicit algorithm is extended to multidimensions. A two-dimensional axisymmetric transonic nozzle flow problem with weak oblique shock is solved.