FE-project

What is this project?

In FE-Project, we develop a library for fluid simulations using the discontinuous Galerkin method (DGM). We also provide sample programs and an atmospheric model for meteorological simulations (SCALE-DG).

• Examples of simulation results from SCALE-DG

For more animations, please see the ''FE-project gallery'' channel on YouTube (url: https://www.youtube.com/channel/UCO17OQtKHwkkQwmHD9y9mQg/featured).

Models with FE library

Nonhydrostatic atmospheric model

• Regional and global models (SCALE-DG)
• Simple 2D model with only dynamical process

Shallow water model

• Global shallow water model using a cubed-sphere mesh

Simple samples for an introduction to DGM

1D problems

• Linear advection equation
  • Various profiles of the advected quantity
  • Eigenvalue analysis
• Linear advection-diffusion equation

2D problems

• Linear advection equation in a rectangular domain
  • Various profiles of the advected quantity and flow
• Linear advection equation in a cubed-sphere domain
• Poisson equation in a rectangular domain with a multigrid method

3D problems

• Linear advection equation in a cubic domain
  • Various profiles of the advected quantity
• Linear advection equation in a cubed-sphere domain
• Euler equation in a cubic domain
  • Test case for the propagation of sound waves with HEVI temporal methods
• Poisson equation in a cubic domain with a multigrid method

Build FE library

Please see ``INSTALL.md''.

Contributors

• Yuta Kawai
• Xuanzhengbo Ren
• Seiya Nishizawa
• Hirofumi Tomita

Acknowledgements

This project is supported by Developing strategies for coupling high-order dynamical core and physics processes considering future high-resolution atmospheric simulations(MEXT KAKENHI Grant Number 25K17471), the Transformative Research Areas B: DNA Climate Science (MEXT KAKENHI Grant Number JP20H05731), Moonshot Goal 8: Realization of a society safe from the threat of extreme winds and rains by controlling and modifying the weather by 2050 (Development of an atmospheric simulation model for probability estimation for local atmospheric phenomena), JICA and JST SATREPS (grant Number: JPMJSA2109), JST AIP Grant Number JPMJCR19U2, and the Foundation for Computational Science (FOCUS) Establishing Supercomputing Center of Excellence. The model development and validation experiments are performed using supercomputers (Oakbridge-CX and Wisteria) at the University of Tokyo and Fugaku at RIKEN (Project IDs: ra000005, hp200271, hp230278).

General references

• Kawai, Y. and H. Tomita, 2025, Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0. Geosci. Model Dev., 18, 725-762.
• Kawai, Y. and H. Tomita, 2023, Numerical accuracy necessary for large-eddy simulation of planetary boundary layer turbulence using discontinuous Galerkin method. Mon. Wea. Rev., 151, 1479-1508