Stable nodal projection method on octree grids
Abstract
We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the viscosity and projection steps, we utilize supra-convergent finite difference approximations with sharp boundary treatments. We demonstrate the stability of our projection on uniform grids, identify a sufficient stability condition on adaptive grids, and validate these findings numerically. We further demonstrate the accuracy and capabilities of our solver with several canonical two- and three-dimensional simulations of incompressible fluid flows. Overall, our method is second-order accurate, allows for dynamic grid adaptivity with arbitrary geometries, and reduces the overhead in code development through data collocation.
Cite
@article{arxiv.2306.09957,
title = {Stable nodal projection method on octree grids},
author = {Matthew Blomquist and Scott R. West and Adam L. Binswanger and Maxime Theillard},
journal= {arXiv preprint arXiv:2306.09957},
year = {2025}
}