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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Cao, Yangyang, Huang, Qian, Koellermeier, Julian, Kurganov, Alexander, Liu, Yongle
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916765594812416
author Cao, Yangyang
Huang, Qian
Koellermeier, Julian
Kurganov, Alexander
Liu, Yongle
author_facet Cao, Yangyang
Huang, Qian
Koellermeier, Julian
Kurganov, Alexander
Liu, Yongle
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_23144
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations
Cao, Yangyang
Huang, Qian
Koellermeier, Julian
Kurganov, Alexander
Liu, Yongle
Numerical Analysis
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.
title Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations
topic Numerical Analysis
url https://arxiv.org/abs/2505.23144