关键词: family of set-valued mapping, nonempty intersection theorem, system of generalized vector equilibrium problem, product G-convex space, shock wave, generation of vortices, finite volume TVD scheme, mesh generation

Abstract: The impingement of a plane shock wave in air on a rectangular or triangular obstacle is simulated numerically with high resolution TVD (total variation diminishing) scheme in finite volume formulation with Schwarz transformation in mesh generation. The mesh lines are quite adaptive to the physical features of the unsteady flow field and concentrate locally near the corners. At the initial stage the flow field is complex, and the scale of viscous diffusion is verr small and the viscosity of fluid in computation may be neglected. The unsteadr generation of concerntrated vortices downstream of the sharp corner as the result of the nonnuiformity of both temperature and entropy fields in ptane.hzviscid compressible fluid, induced by bow shock wave. is shown clearly and in accordance with optical measurements, performed by our request.

Key words: family of set-valued mapping, nonempty intersection theorem, system of generalized vector equilibrium problem, product G-convex space, shock wave, generation of vortices, finite volume TVD scheme, mesh generation