Research Summaries

Back Conservative and Positivity-Preserving CG/DG Nonhydrostatic Atmospheric Model

Fiscal Year 2019
Division Graduate School of Engineering & Applied Science
Department Applied Mathematics
Investigator(s) Giraldo, Francis X.
Kozdon, Jeremy E.
Sponsor Office of Naval Research (Navy)
Summary We propose to extend the Nonhydrostatic Unified Model of the Atmosphere (NUMA) to be: (1) mass conserving, (2) entropy stable, and (3) positivity preserving, all while remaining highly efficient and amenable to adaptive (grid) methods. For reasons that are obvious we absolutely require NUMA to be mass-conserving. However, entropy-stability is a less well-known trait which means that the numerics will never break, without the need to add artificial diffusion. Positivity preservation is important, in particular, for tracer transport and we plan to achieve this by exploring both semi-Lagrangian methods in addition to purely spatial methods. The efficiency of NUMA will be achieved through the use of time-integration methods that require few global system solves while allowing for very large explicit time-steps. We will also explore the construction of adaptive methods that are both mass conserving and (up to time-truncation) energy conserving. Finally, we will test all of these new developments on challenging LES problems.
Keywords
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Data Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal