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arXiv · 2602.02247

A new Energy Equation Derivation for the Shallow Water Linearized Moment Equations

Julian Koellermeier
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Abstract

Shallow Water Moment Equations (SWME) are extensions to the well-known Shallow Water Equations (SWE) for the efficient modeling and numerical simulation of free-surface flows. While the SWE typically assume a depth-averaged vertical velocity profile, the SWME allow for vertical variations of the velocity profile. The SWME therefore assume a polynomial profile and then derive additional evolution equations for the polynomial coefficients via higher order depth integration. In this work, we perform a new systematic derivation of the energy equation for a specific variant of the SWME, called the Shallow Water Linearized Moment Equations (SWLME). The derivation is based on the standard SWE energy equation derivation and includes the skew-symmetric formulation of the model. The new systematic derivation is beneficial for the extension to other SWME variants and their numerical solution.

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Julian Koellermeier. 2026-02-02. A new Energy Equation Derivation for the Shallow Water Linearized Moment Equations. https://arxiv.org/abs/2602.02247

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