SoftwareApplication
name: Variational Multiscale code base, supporting the publication: Structure-preserving Variational Multiscale Stabilization of the Incompressible Navier-Stokes Equations
description: Variational Multiscale code base, supporting the publication: Structure-preserving Variational Multiscale Stabilization of the Incompressible Navier-Stokes Equations
description: An implementation of my Variational Multiscale formulation for the vorticity-velocity-pressure formulation of the incompressible Navier-Stokes equations, writen in Nutils, an open-source finite element package written in Python. The following folders are of interest: /NavierStokes (Main folder): Contains the scripts where we implemented the current formulation. In main.py, almost all test cases, with various parameters can be ran, but this only runs a single simulation. It is suggested to start here.There are various other files, that either run multiple simulations for a specific reason (e.g. convergence analysis), or generate images for the paper, or intermediate simulation results (either plain text output files, .csv files, or final images)/OseenEquation (Somewhat interesting): We started by analyzing the Oseen equations. This folder contains many early ideas and results. None of these made it to the final paper. The remaining folders contain data backups, data from the DELFTBLUE cluster, or scrap code from initial testing/trying different ideas from various papers. This has been added for completeness, but most likely will not contain any interesting results.
code repository: https://data.4tu.nl/v3/datasets/e0d59975-9c8e-4127-8087-8a35e9063234.git
author: https://orcid.org/0009-0002-4324-1122
keywords: incompressible Navier-Stokes
keywords: Numerical analysis
keywords: finite element method
keywords: variational multiscale stabilization
programming language: Other
programming language: Python
license:
  creative work: creativeWork
    name: MIT
reference publication: arxiv.2512.14231

https://orcid.org/0009-0002-4324-1122
type: Person
given name: Kevin
family name: Dijkstra
name: Kevin Dijkstra

arxiv.2512.14231
type: ScholarlyArticle
name: Structure-preserving Variational Multiscale Stabilization of the Incompressible Navier-Stokes Equations
url: https://doi.org/10.48550%2Farxiv.2512.14231