On the Numerical Solution of Two-Dimensional, Laminar Compressible Flows With Imbedded Shock Waves

The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps. Sample solutions are presented for supersonic flow of air over the leading edge of a slightly blunted flat plate, past a backward facing step, and in the near wake of a blunt trailing edge. Free-stream Mach numbers from 2 to 10 are included in the sample computations.