Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations

TL;DR

This paper introduces second-order flux globalization based well-balanced path-conservative central-upwind schemes for hyperbolic shallow water linearized moment equations, effectively preserving steady states and handling complex free-surface flows.

Contribution

It develops a novel flux globalization approach for path-conservative schemes applied to shallow water moment equations, ensuring well-balanced properties for complex steady states.

Findings

Accurately preserves steady states including moving-water solutions.

Performs reliably on benchmarks like dam-break and smooth solutions.

Demonstrates robustness for nonlinear, nonconservative shallow water models.

Abstract

We develop second-order path-conservative central-upwind (PCCU) schemes for the hyperbolic shallow water linearized moment equations (HSWLME), which are an extension of standard depth-averaged models for free-surface flows. The proposed PCCU schemes are constructed via flux globalization strategies adapted to the nonconservative form via a path-conservative finite-volume method. The resulting scheme is well-balanced (WB) in the sense that it is capable of exactly preserving physically relevant steady states including moving-water ones. We validate the proposed scheme on several benchmarks, including smooth solutions, small perturbation of steady states, and dam-break scenarios. These results demonstrate that our flux globalization based WB PCCU schemes provide a reliable framework for computing solutions of shallow water moment models with nonlinear and nonconservative features.