CMX Student/Postdoc Seminar
I will present a spectral scheme for the numerical solution of shock-wave problems in general non-periodic domains. The approach utilizes the Fourier Continuation (FC) method for spectral representation of non-periodic functions in general domains in conjunction with smooth localized artificial viscosity assignments produced by means of a Shock-Detecting Neural Network (SDNN). The minimally invasive neural net-induced viscous term eliminates Gibbs ringing while enabling spectral dispersionless flows, and, unlike most other approaches, it does not suffer from unphysical spurious oscillations over smooth flow regions. The FC-SDNN algorithm, which relies on a Mach number proxy for neural-network analysis of the solution's regularity, generally provides accurate resolution of discontinuities, as well as significantly smoother profiles away from jump discontinuities than those produced by other methods, including ENO/WENO solvers, Godunov schemes and other finite volume and artificial viscosity approaches. The character of the method will be demonstrated by means of applications to a number of important test cases, including a Mach 3 wind-tunnel step problem, a Double Mach ramp reflection of a shock, a shock-vortex interaction, and a Blast wave problem, among others.