A Geometric Approach Towards Momentum Conservation
Numerical Analysis
2013-04-26 v1
Abstract
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we treat conservation of momentum as a tensor equation and describe a higher order approximation to this tensor equation. The resulting scheme satisfies mass and momentum conservation laws exactly, and resembles a staggered-mesh finite-volume method. Numerical test-cases to which the discretization scheme is applied are the Kovasznay flow, and lid-driven cavity flow.
Keywords
Cite
@article{arxiv.1304.6991,
title = {A Geometric Approach Towards Momentum Conservation},
author = {D. Toshniwal and R. H. M. Huijsmans and M. I. Gerritsma},
journal= {arXiv preprint arXiv:1304.6991},
year = {2013}
}