Direct Numerical Simulations of Film Cooling in a Supersonic Boundary-Layer Flow on Massively-Parallel Supercomputers

Future rocket-nozzle extensions have to be thermally protected by a film of cooling gas. Here, the cooling film is generated by wall-parallel cooling-gas injection through a backward facing step. In a first step, a generic laminar flat-plate boundary-layer flow with external Mach number 2.6 and zero streamwise pressure gradient is used, where air is employed as hot and cooling gas. Direct numerical simulations are performed allowing for the reliable detection of any enhanced laminar-flow instability. Using compact finite differences or compact data filtering, tridiagonal sets of equations have to be solved employing the pipelined Thomas algorithm in order to compute various spatial derivatives or low-pass filtered data. In contrast to the NEC-SX8/9 vector machines with few, powerful compute nodes the solution of this tridiagonal systems turned out to be a major bottleneck on the massively parallel Cray-XE6 system. In order to avoid processor idling fully explicit and sub-domain compact finite differences are implemented and applied to the wall-parallel cooling-gas injection problem. The numerical results and performance data on the CRAY-XE6 system are compared to the regular, globally compact finite-difference scheme.