Multiscale Modeling Framework using Element-based Galerkin Methods for Moist Atmospheric Limited-Area Simulations

TL;DR

The paper introduces a multiscale modeling framework (MMF) for moist atmospheric limited-area simulations that couples large-scale processes on a coarse grid with explicit small-scale cloud processes on multiple fine grids, all governed by the same nonhydrostatic compressible Navier–Stokes equations discretized with a high-order spectral-element method. A unified dynamical core enables consistent LSP/SSP modeling, with coupling achieved through horizontal averaging and forcing/feedback terms, while nonconforming vertical grids allow vertical refinement. Temporal integration uses a second-order IMEX ARK2 scheme, and the framework is implemented in an object-oriented NUMA-based code (xNUMA) with MPI parallelism, enabling SSPs to run locally per LSP column. Numerical results on 2D squall-line and 3D supercell tests show that MMF improves the representation of moist dynamics and cloud processes compared to a coarse standard model, notably in precipitation patterns and cold-pool structure. The study highlights higher arithmetic intensity for MMF, suggesting favorable performance on future exascale architectures and outlines directions for cost reduction and GPU/ROM enhancements.

Abstract

This paper presents a multiscale modeling framework (MMF) to model moist atmospheric limited-area weather. The MMF resolves large-scale convection using a coarse grid while simultaneously resolving local features through numerous fine local grids and coupling them seamlessly. Both large- and small-scale processes are modeled using the compressible Navier-Stokes equations within the Nonhydrostatic Unified Model of the Atmosphere (NUMA), and they are discretized using a continuous element-based Galerkin method (spectral elements) with high-order basis functions. Consequently, the large-scale and small-scale models share the same dynamical core but have the flexibility to be adjusted individually. The proposed MMF method is tested in 2D and 3D idealized limited-area weather problems involving storm clouds produced by squall line and supercell simulations. The MMF numerical results showed enhanced representation of cloud processes compared to the coarse model.

Figures (15)

• Figure 1: Decomposition of the scales modeled via MMF along the wavenumber axis.
• Figure 2: Configuration of the LSP and SSP grids for MMF.
• Figure 3: Coupling of nonconforming LSP and SSP grids for MMF.
• Figure 4: Layouts of domain decomposition for limited-area models. ($N_{proc,x}$ and $N_{proc,y}$ are the number of processors in the $x$ and $y$ directions.)
• Figure 5: Dimensions of a grid partition assigned to an MPI rank and the number of elements along each direction. ($N_{ex}$, $N_{ey}$, and $N_{ez}$ are the number of elements along the $x,y,z$ directions.)