Complex conservative difference schemes for computing supersonic flows past simple aerodynamic forms

Complex conservative modifications of two-dimensional difference schemes on a minimum stencil are presented for the Euler equations. The schemes are conservative with respect to the basic divergent variables and the divergent variables for spatial derivatives. Approximations of boundary conditions for computing flows around variously shaped bodies (plates, cylinders, wedges, cones, bodies with cavities, and compound bodies) are constructed without violating the conservation properties in the computational domain. Test problems for computing flows with shock waves and contact discontinuities and supersonic flows with external energy sources are described.