Efficient and scalable atmospheric dynamics simulations using non-conforming meshes

TL;DR

The paper addresses the challenge of fast, scalable atmospheric simulations with multi-scale dynamics by employing a $h$-adaptive Discontinuous Galerkin (DG) discretization and an IMEX-RK time integrator, tailored for low Mach number flows ($M$) and Froude number $Fr$. It demonstrates that non-conforming refinement around orography yields comparable accuracy to uniform meshes while reducing computational cost, thanks to data-locality and matrix-free implementation in the deal.II framework. The results show substantial wall-clock savings (approximately a 93% reduction) and favorable strong scaling up to thousands of cores on EuroHPC hardware, with shared-node effects and solver components identified as key factors for future improvement. The work supports advancing toward operational numerical weather prediction with adaptive, high-order methods, and outlines extensions to moist physics and spherical geometries.

Abstract

We present the massively parallel performance of a $h$-adaptive solver for atmosphere dynamics that allows for non-conforming mesh refinement. The numerical method is based on a Discontinuous Galerkin (DG) spatial discretization, highly scalable thanks to its data locality properties, and on a second order Implicit-Explicit Runge-Kutta (IMEX-RK) method for time discretization, particularly well suited for low Mach number flows. Simulations with non-conforming meshes for flows over orography can increase the accuracy of the local flow description without affecting the larger scales, which can be solved on coarser meshes. We show that the local refining procedure has no significant impact on the parallel performance and, therefore, both efficiency and scalability can be achieved in this framework.

Figures (5)

• Figure 1: 3D medium-steep bell-shaped hill test case, non conforming mesh. $x-z$ slice at $y = 20km$.
• Figure 2: Vertical velocity in the 3D medium-steep bell-shaped hill test case at $T_{f} = 10h$, $x-y$ slice at $z = 800m$. Contours in the range $[parse-numbers=false]{[-1.5, 1.3]}{\meter\per\second}$ with a $0.1m\per s$ interval. Top: comparison between the uniform mesh (black lines) and the non-conforming mesh (red lines). Negative contours are dashed. Bottom: absolute difference between the uniform mesh and the non-conforming mesh.
• Figure 3: As in Figure \ref{['fig:3D_contours_xy']}, but showing an $x-z$ slice at $y = 20km$, and contours in the range $[parse-numbers=false]{[-2.25, 2]}{\meter\per\second}$ with a $0.2m\per s$ interval.
• Figure 4: Strong scaling analysis. Computed speedup as a function of the number of cores used in the simulations with the uniform mesh using polynomial degree $4$ (solid black lines) and polynomial degree $2$ (dashed blue lines), and with the non-conforming mesh (dashed red lines). Top: exclusive use of computational nodes. Bottom: shared use of computational nodes.
• Figure 5: