On the outflow conditions for spectral solution of the viscous blunt-body problem
The authors examine some different outflow boundary conditions in simulating viscous supersonic/hypersonic flows over blunt bodies by means of spectral collocation methods to identify appropriate ones for obtaining accurate solutions in the whole flow field. The dual composition of the outflow boundary conditions necessitates individual treatments in each part. For the supersonic portion, the authors use the proper compatibility equations with viscous consideration. At the subsonic portion, where a flow condition from the unknown downstream is required, miscellaneous techniques are proposed. These include (1) removing streamwise pressure gradient partly or completely, (2) sublayer approximation, (3) utilizing inviscid solution of the same problem, (4) boundary non-reflectivity condition, (5) extrapolation of all primitive variables and (6) extrapolating the pressure along with using proper compatibility relations. A verification procedure is suggested to investigate the accuracy and performance of each of the above outflow techniques in shrinking/extending body geometry. As the paper is organized to be self-contained, a quick look at the governing equations, boundary conditions and numerical method is given. After that, the above techniques for resolving subsonic outflow boundary conditions are studied in detail with their advantages and disadvantages. A hypersonic viscous flow of Mach 5.73 over a circular cylinder is considered as the model problem. Experimental and numerical comparisons are made to suggest the most proper method for stable convergent solution for the model problem with adiabatic or isothermal surface conditions. Then, a hypersonic viscous flow at Mach 15 over a parabola is computed to examine the accuracy of the proposed subsonic outflow boundary conditions. Finally, the authors sum up and draw conclusions.
scientific article; zbMATH DE number 5566331
scientific article