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Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

Kees, Chris·Guermond, Jean-Luc·Popov, Bojan·Tovar, Eric Joseph
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Abstract

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

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97 MATHEMATICS AND COMPUTINGSerreSerre–Green-Naghdiconvex limitingentropy viscosityfinite element methodinvariant domainpositivity-preservingsecond-order accuracyshallow waterwell-balanaced approximation

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Kees, Chris, Guermond, Jean-Luc, Popov, Bojan, Tovar, Eric Joseph. 2022-06-27. Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations. https://doi.org/10.1007/s42286-022-00062-8

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