Adaptive Mesh Refinement (AMR) for the Solution of Compressible Euler Equations Using the Discontinuous Galerkin Method.

In this oral presentation, we delve into our efforts aimed at enhancing a Numerical Weather Prediction (NWP) models through the integration of dynamic Adaptive Mesh Refinement (AMR) capabilities, which proves to be more efficient than the widely adopted nesting methods, both one- and two-way. The incorporation of AMR holds promising advantages, including increased resolution in specific regions of interest, decreased computational overhead compared to high-resolution regional models, and improved tracking of extreme weather phenomena such as hurricanes and tropical cyclones.

Our current work involves an exploration of both static and dynamic AMR techniques applied to solve the compressible Euler equations, which are commonly employed in non-hydrostatic dynamical cores. We have implemented an oct-tree based AMR approach for two distinct methods: the finite-volume (FV) method, utilized in NOAA's FV3 dycore, and the high-order discontinuous Galerkin (DG) method. While AMR implementation in the FV method follows a relatively straightforward path, the latter demands meticulous computation of the numerical flux at cell boundaries to ensure the method's local and global conservation properties remain intact.

This presentation will encompass the dissemination of results derived from a range of test cases designed to validate the precision of the implementation in both box-based and spherical contexts. Given the atmosphere's stratification, it's commonplace to apply 2D refinement in horizontal directions while keeping the number of vertical levels constant. Test cases encompass fundamental scenarios such as scalar advection, buoyancy-driven flows within a box, and acoustic wave propagation on the sphere. Comprehensive insights into the performance of dynamic AMR and the resulting computational cost reductions will be shared.

In essence, this presentation sheds light on our efforts to empower an NWP model with dynamic AMR capabilities, transcending conventional nesting methods. Through careful implementation and rigorous testing, we ascertain the viability of this approach for refining weather prediction models and enhancing our understanding of atmospheric dynamics.