Kinetic framework with consistent hydrodynamics for shallow water equations

TL;DR

This paper introduces a new kinetic modeling framework for shallow water equations that accurately captures viscous effects and offers enhanced control and stability for numerical solutions.

Contribution

It presents a novel discrete velocity kinetic framework that consistently recovers viscous shallow water equations with improved force handling and dissipation control.

Findings

Accurate recovery of viscous shallow water equations.

Enhanced stability and control in numerical simulations.

No errors in dissipation rates during modeling.

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.