TimestepperTestCases.jl

TimestepperTestCases.jl is a Julia package that provides test cases and diagnostics for evaluating time-stepping schemes in free-surface ocean models. This repository complements the paper "A Low-Storage Runge-Kutta Framework for Non-Linear Free-Surface Ocean Models" by providing:

• Three idealized test cases spanning linear to fully turbulent regimes
• Exact variance budget diagnostics for quantifying numerical mixing
• Linear stability analysis tools
• Notebooks for reproducing figures and analysis from the paper

Overview

This package implements test cases designed to highlight differences in performance between time discretization schemes, particularly comparing low-storage Runge-Kutta (RK) methods with Adams-Bashforth (AB2) schemes. The test cases include:

1. Internal Tide: A linear test case isolating temporal discretization effects
2. Idealized Coastal Baroclinic Adjustment: A nonlinear case demonstrating submesoscale variability
3. Equilibrated Channel Flow: A long-term equilibrated configuration showing interaction between numerical and physical mixing

Key Features

• Exact Variance Budgets: Diagnostics that are exact locally in both space and time, enabling quantification of numerical mixing from time discretization
• Multiple Timesteppers: Support for QuasiAdamsBashforth2, SplitRungeKutta3, and SplitRungeKutta4
• Free Surface Options: Both implicit and split-explicit free surface formulations
• Comprehensive Diagnostics: Reference potential energy (RPE), available potential energy (APE), kinetic energy, and numerical diffusivity diagnostics

Quick Links

• Getting Started - Installation and basic usage
• Experiments - Detailed descriptions of the three test cases
• Diagnostics - Understanding variance budgets and numerical mixing
• Stability Analysis - Linear stability analysis tools
• Notebooks - Reproducing figures and analysis
• API Reference - Complete function documentation

Citation

If you use this package in your research, please cite the associated paper:

@article{silvestri2025timestepper,
  title={A Low-Storage Runge-Kutta Framework for Non-Linear Free-Surface Ocean Models},
  author={Silvestri, Simone and others},
  journal={Journal of Advances in Modeling Earth Systems},
  year={2025}
}

Related Packages

This package builds on Oceananigans.jl, a fast, friendly, flexible ocean-flavored fluid dynamics package for CPUs and GPUs.