Kinetic framework with consistent hydrodynamics for shallow water equations
Fluid Dynamics
2025-05-13 v1
Abstract
We present a novel discrete velocity kinetic framework to consistently recover the viscous shallow water equations. The proposed model has the following fundamental advantages and novelties: (a) A novel interpretation and general framework to introduce forces, (b) the possibility to consistently split pressure contributions between equilibrium and a force-like contribution, (c) consistent recovery of the viscous shallow water equations with no errors in the dissipation rates, (d) independent control over bulk viscosity, and (e) consistent second-order implementation of forces. As shown through a variety of different test cases, these features make for an accurate and stable solution method for the shallow-water equations.
Cite
@article{arxiv.2505.06697,
title = {Kinetic framework with consistent hydrodynamics for shallow water equations},
author = {S. A. Hosseini and I. V. Karlin},
journal= {arXiv preprint arXiv:2505.06697},
year = {2025}
}