Compressible Euler Extension of a Massively-Parallel Spectral Element Solver

Current supercomputing systems have tens or hundreds of thousands of cores and are trending to GPU and co-compute platforms that deliver thousands of cores per node. Modern computational fluid dynamics codes must be designed to take advantage of these developments in order to further their use in the design cycle. Furthermore, these codes must be highly accurate, stable, and geometrically flexible. NEK5000 is a massively-parallel spectral element code that exhibits these characteristics but currently only for incompressible and low-Mach flows. Adding capabilities for NEK5000 to solve the fully compressible Navier-Stokes equations will extend its usefulness to aerospace applications. As a first step the following work extends NEK5000’s capabilities to solve the 2D compressible Euler equations. Using the conservative formulation, the equations are discretized using a non-staggered spectral element mesh, and the state variables are advanced using 1st order explicit Euler time stepping. A channel with a 10% bump is used as a test case for the modification. The modified NEK5000 code performs very well despite not being optimized for use in hyperbolic equations.