A new Energy Equation Derivation for the Shallow Water Linearized Moment Equations
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908805810356224 |
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| author | Koellermeier, Julian |
| author_facet | Koellermeier, Julian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new Energy Equation Derivation for the Shallow Water Linearized Moment Equations Koellermeier, Julian Numerical Analysis Analysis of PDEs Fluid Dynamics 35L60, 35B38, 76Bxx 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. |
| title | A new Energy Equation Derivation for the Shallow Water Linearized Moment Equations |
| topic | Numerical Analysis Analysis of PDEs Fluid Dynamics 35L60, 35B38, 76Bxx |
| url | https://arxiv.org/abs/2602.02247 |