arXiv subjects

Thomas Bendall

Publications and source records attributed to Thomas Bendall.

6 recordsLinked to original sources

arXiv2026

Splitting horizontal and vertical polynomial order in a compatible finite element discretisation for numerical weather prediction

The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical motions occur on very different length scales, motivating numerical discretisations that can reflect this structure. In this study, we introduce a compatible finite element discretisation of the compressible Boussinesq and compressible Euler equations in which the horizontal and vertical polynomial orders are treated independently. The split-order discretisation is constructed using a tensor-product framework that preserves the discrete de Rham complex and associated mimetic properties. Its wave-propagation characteristics are examined through a discrete dispersion analysis that extends previous analyses to configurations with differing horizontal and vertical polynomial orders. The results show that increasing horizontal order improves the representation of gravity waves at low and intermediate wavenumbers, while increasing vertical order can degrade dispersion accuracy near the grid scale and introduce spectral gaps. A series of idealised numerical experiments, including gravity-wave propagation, advective transport, mountain-wave flow, and a global baroclinic-wave test, is used to assess the scheme's accuracy and convergence properties. These experiments demonstrate that increasing the polynomial order in the dominant direction of motion improves convergence, and that increasing the horizontal order yields the greatest gain in accuracy under typical atmospheric conditions. The results indicate that split-order compatible finite element discretisations provide a viable alternative for controlling accuracy and numerical behaviour in atmospheric dynamical cores.

math.NA↗

arXiv2025

Fast-wave slow-wave spectral deferred correction methods applied to the compressible Euler equations

This paper investigates the application of a fast-wave slow-wave spectral deferred correction time-stepping method (FWSW-SDC) to the compressible Euler equations. The resulting model achieves arbitrary order accuracy in time, demonstrating robust performance in standard benchmark idealised test cases for dynamical cores used for numerical weather prediction. The model uses a compatible finite element spatial discretisation, achieving good linear wave dispersion properties without spurious computational modes. A convergence test confirms the model's high temporal accuracy. Arbitrarily high spatial-temporal convergence is demonstrated using a gravity wave test case. The model is further extended to include the parametrisation of a simple physics process by adding two phases of moisture and its validity is demonstrated for a rising thermal problem. Finally, a baroclinic wave in simulated in a Cartesian domain.

math.NA↗

arXiv2025

A regional implementation of a mixed finite-element, semi-implicit dynamical core

This paper explores how to adapt a new dynamical core to enable its use in one-way nested regional weather and climate models, where lateral boundary conditions (LBCs) are provided by a lower-resolution driving model. The dynamical core has recently been developed by the Met Office and uses an iterated-semi-implicit time discretisation and mixed finite-element spatial discretisation. The essential part of the adaptation is the addition of the LBCs to the right-hand-side of the linear system which solves for pressure and momentum simultaneously. The impacts on the associated Helmholtz preconditioner and multigrid techniques are also described. The regional version of the dynamical core is validated through big-brother experiments based on idealised dynamical core tests. These experiments demonstrate that the subdomain results are consistent with those from the full domain, confirming the correct application of LBCs. Inconsistencies arise in cases where the LBCs are not perfect, but it is shown that the application of blending can be used to overcome these problems.

physics.flu-dyn↗

arXiv2024

The impact of the explicit representation of convection on the climate of a tidally locked planet in global stretched-mesh simulations

Convective processes are crucial in shaping exoplanetary atmospheres but are computationally expensive to simulate directly. A novel technique of simulating moist convection on tidally locked exoplanets is to use a global 3D model with a stretched mesh. This allows us to locally refine the model resolution to 4.7 km and resolve fine-scale convective processes without relying on parameterizations. We explore the impact of mesh stretching on the climate of a slowly rotating TRAPPIST-1e-like planet, assuming it is 1:1 tidally locked. In the stretched-mesh simulation with explicit convection, the climate is 5 K colder and 25% drier than that in the simulations with parameterized convection (with both stretched and quasi-uniform meshes)}. This is due to the increased cloud reflectivity - because of an increase of low-level cloudiness - and exacerbated by the diminished greenhouse effect due to less water vapor. At the same time, our stretched-mesh simulations reproduce the key characteristics of the global climate of tidally locked rocky exoplanets, without any noticeable numerical artifacts. Our methodology opens an exciting and computationally feasible avenue for improving our understanding of 3D mixing in exoplanetary atmospheres. Our study also demonstrates the feasibility of a global stretched mesh configuration for LFRic-Atmosphere, the next-generation Met Office climate and weather model.

astro-ph.EP↗

arXiv2024

A mixed finite-element, finite-volume, semi-implicit discretisation for atmospheric dynamics: Spherical geometry

The reformulation of the Met Office's dynamical core for weather and climate prediction previously described by the authors is extended to spherical domains using a cubed-sphere mesh. This paper updates the semi-implicit mixed finite-element formulation to be suitable for spherical domains. In particular the finite-volume transport scheme is extended to take account of non-uniform, non-orthogonal meshes and uses an advective-then-flux formulation so that increment from the transport scheme is linear in the divergence. The resulting model is then applied to a standard set of dry dynamical core tests and compared to the existing semi-implicit semi-Lagrangian dynamical core currently used in the Met Office's operational model.

math.NA↗

arXiv2023

Simulations of idealised 3D atmospheric flows on terrestrial planets using LFRic-Atmosphere

We demonstrate that LFRic-Atmosphere, a model built using the Met Office's GungHo dynamical core, is able to reproduce idealised large-scale atmospheric circulation patterns specified by several widely-used benchmark recipes. This is motivated by the rapid rate of exoplanet discovery and the ever-growing need for numerical modelling and characterisation of their atmospheres. Here we present LFRic-Atmosphere's results for the idealised tests imitating circulation regimes commonly used in the exoplanet modelling community. The benchmarks include three analytic forcing cases: the standard Held-Suarez test, the Menou-Rauscher Earth-like test, and the Merlis-Schneider Tidally Locked Earth test. Qualitatively, LFRic-Atmosphere agrees well with other numerical models and shows excellent conservation properties in terms of total mass, angular momentum and kinetic energy. We then use LFRic-Atmosphere with a more realistic representation of physical processes (radiation, subgrid-scale mixing, convection, clouds) by configuring it for the four TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) scenarios. This is the first application of LFRic-Atmosphere to a possible climate of a confirmed terrestrial exoplanet. LFRic-Atmosphere reproduces the THAI scenarios within the spread of the existing models across a range of key climatic variables. Our work shows that LFRic-Atmosphere performs well in the seven benchmark tests for terrestrial atmospheres, justifying its use in future exoplanet climate studies.

astro-ph.EP↗