Conservative invariant finite-difference schemes for the modified shallow water equations in Lagrangian coordinates
Numerical Analysis
2023-04-18 v1 Numerical Analysis
Abstract
The one-dimensional modified shallow water equations in Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian coordinates, in mass Lagrangian variables, and Eulerian coordinates. For equations in Lagrangian coordinates an invariant finite-difference scheme is constructed for all cases for which conservation laws exist in the differential model. Such schemes possess the difference analogues of the conservation laws of mass, momentum, energy, the law of center of mass motion for horizontal, inclined and parabolic bottom topographies. Invariant conservative difference scheme is tested numerically in comparison with naive approximation invariant scheme.
Keywords
Cite
@article{arxiv.2111.08604,
title = {Conservative invariant finite-difference schemes for the modified shallow water equations in Lagrangian coordinates},
author = {V. A. Dorodnitsyn and E. I. Kaptsov and S. V. Meleshko},
journal= {arXiv preprint arXiv:2111.08604},
year = {2023}
}
Comments
30 pages, 12 figures