Predicting mesh density for adaptive modelling of the global atmosphere

Area of Science:

• Numerical analysis
• Atmospheric science
• Computational fluid dynamics

Background:

• Solving complex fluid dynamics problems like the shallow water equations requires efficient numerical methods.
• Traditional uniform meshes can be computationally expensive, especially for simulations with evolving high-resolution features.
• Mesh adaptation strategies aim to optimize computational resources by concentrating grid points where they are most needed.

Purpose of the Study:

• To develop and evaluate an infrequent mesh adaptation strategy for solving the shallow water equations on a spherical grid.
• To reduce the computational cost associated with mesh adaptation and load balancing in numerical weather prediction models.
• To improve the accuracy of simulations by allowing more computational resources for mapping the solution.

Main Methods:

• Solving the shallow water equations on a spherical mesh that adapts infrequently based on predicted future solutions.
• Implementing an adaptation criterion primarily based on the gradient of vorticity.
• Utilizing a coarse mesh prediction to estimate the evolution of high-resolution features.

Main Results:

• An infrequent mesh adaptation (every 12 hours) resulted in a mesh with approximately 20% of the cells compared to a uniform mesh, yielding equivalent results.
• The adaptation criterion, balancing resolved and unresolved features, effectively managed mesh density.
• This approach demonstrated efficiency comparable to studies using much more frequent adaptation intervals.

Conclusions:

• Infrequent mesh adaptation is a computationally efficient strategy for solving the shallow water equations.
• Predictive mesh density based on coarse mesh solutions balances large-scale dynamics and fine-scale feature resolution.
• This method offers a cost-effective way to achieve accurate simulations in atmospheric and oceanic modeling.