Numerical simulation of standing solitons and their interaction

Standing soliton was studied by numerical simulation of ifs governing equation, a cubic Schrodiger equation with a complex conjugate term, which was derived by Miles and was accepted. The value of linear damping in Miles equation was studied. Calculations showed that linear damping effects strongly on the formation of a standing soliton and Laedke and Spatschek stable condition is only a necessary condition, but not a sufficient one. The interaction of two standing solitons was simulated. Simulations showed that the interaction pattern depends on system parameters. Calculations for the different initial condition and its development indicated that a stable standing soliton can be fanned only for proper initial disturbance, otherwise the disturbance will disappear or develop into several solitons.

Analysis of super compact finite difference method and application to simulation of vortex-shock interaction

Turbulence and aeroacoustic noise high-order accurate schemes are required, and preferred, for solving complex flow fields with multi-scale structures. In this paper a super compact finite difference method (SCFDM) is presented, the accuracy is analysed and the method is compared with a sixth-order traditional and compact finite difference approximation. The comparison shows that the sixth-order accurate super compact method has higher resolving efficiency. The sixth-order super compact method, with a three-stage Runge-Kutta method for approximation of the compressible Navier-Stokes equations, is used to solve the complex flow structures induced by vortex-shock interactions. The basic nature of the near-field sound generated by interaction is studied.