Massively-parallel Spectral Element Algorithm Development for High Speed Flows

The need to reduce both the time and cost of product design has allowed numerical analysis to play an ever-increasing role in design cycle analysis. This is particularly true in the aerospace industry, where the use of computational fluid dynamics can help reduce the need for costly prototype testing. Due to the extremely high computational costs associated with simulating complex industrial flows directly, most modern simulation tools employ solvers that rely heavily on turbulence modeling. However, the combination of modern supercomputers and algorithms that can take full advantage of them allows for higher fidelity solvers, with reduced dependence on turbulence modeling, to be included in design cycle analysis.

This work employs the discontinuous Galerkin spectral element method in a solver designed for high fidelity simulations in the subsonic and transonic flow regimes. The algorithm is implemented using NEK5000, an open-source incompressible spectral element solver, as a code base. Details of the algorithm are given, and the code is validated against several canonical inviscid and viscous test cases. The validation cases show that the code is accurate, stable, and a good performer on supercom- puters. The new solver is then used to study the effectiveness of a cylindrical film cooling hole. The results show a much improved prediction capability of film cooling effectivness as compared to previous low-Mach simulation results. The algorithm is proven to produce quality large-eddy simulation data in a time frame accessible for design cycle analysis. At the end, a suggested direction for future development of the algorithm is discussed, with a focus on how to improve the stability and performance of the solver.