Nonlinear wave packet simulation for a cone at Mach 10 using a GPU accelerated pseudo-spectral scheme

A high-resolution Direct Numerical Simulation (DNS) was carried out to investigate the nonlinear development of a three-dimensional wave packet in a Mach 10 boundary layer on a 7^◦ half-angle straight (right) cone with a “sharp” nose tip at zero angle of attack. The nonlinear wave packet was generated by a short-duration pulse. For the simulation the same cone geometry and flow conditions as in the experiments at the Arnold Engineering Development Complex (AEDC) Hypervelocity Wind Tunnel No. 9 (T9) were used. Resolving the late nonlinear stages and ultimately the development of turbulent spots require highly-resolved DNS. In particular a sufficiently fine grid spacing in the azimuthal direction is needed in order to accurately capture the previously observed “explosive” spectral broadening when the wave packet reaches the late nonlinear stages. In addition, for the development of a turbulent spot the often employed symmetry condition in the azimuthal direction has to be abandoned, thus increasing the computational expense by a factor of two. In order to mitigate the increase of the computational cost of such highly-resolved DNS, a pseudo-spectral discretization in the azimuthal direction using Fast-Fourier-Transfromations (FFT) that are accelerated by employing Graphics Processing Units (GPUs) was developed and validated. This GPU accelerated pseudo-spectral discretization was then implemented into an existing compressible Navier-Stokes solver to carry out a DNS of the nonlinear development of a three-dimensional wave packet on a straight cone at Mach 10.