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arXiv · 2505.06697

Kinetic framework with consistent hydrodynamics for shallow water equations

S. A. Hosseini·I. V. Karlin
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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.

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S. A. Hosseini, I. V. Karlin. 2025-05-10. Kinetic framework with consistent hydrodynamics for shallow water equations. https://arxiv.org/abs/2505.06697

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