Geofluid Object Workbench (GeoFLOW) for Atmospheric Dynamics in the Approach to Exascale: Spectral Element Formulation and CPU Performance

A new software framework using a well-established high-order spectral element discretization is presented for solving the compressible Navier-Stokes equations for purposes of research in atmospheric dynamics in bounded and unbounded limited-area domains, with a view toward capturing spatiotemporal intermittency that may be particularly chal-lenging to attain using low-order schemes. A review of the discretization is provided, emphasizing properties such as the matrix product formalism and other design considerations that will facilitate its effective use on emerging exascale plat-forms, and a new geometry-independent, element boundary exchange method is described to maintain continuity. A vari-ety of test problems are presented that demonstrate accuracy of the implementation primarily in wave-dominated or transitional flow regimes; conservation properties are also demonstrated. A strong scaling CPU study in a three-dimensional domain without using threading shows an average parallel efficiency of ?99% up to 2 3 104 MPI tasks that is not affected negatively by expansion polynomial order. On-node performance is also examined and reveals that, while the primary numerical operations achieve their theoretical arithmetic intensity, the application performance is largely limited by available memory bandwidth. SIGNIFICANCE STATEMENT: This work considers the need for computationally efficient, high-order, low dissipa-tion numerics to fully leverage emerging exascale computing resources in an effort to examine and improve the accu-racy of numerical treatments of atmospheric and weather phenomena. A new spectral element implementation is introduced that attempts to address the issues involved. Well-understood tests are presented that illustrate the known efficacy of the method in wave-dominated, quasi-laminar, and relatively strong shear flow regimes, and good conserva-tion properties for mass and total energy are achieved. Importantly, the implementation is shown to exhibit encourag-ing performance characteristics.