{"title":"适用于任意截面渠道的一维增强浅水方程系统","authors":"A. Valiani, V. Caleffi","doi":"10.1016/j.advwatres.2024.104735","DOIUrl":null,"url":null,"abstract":"<div><p>This work provides a new formulation of the one-dimensional <em>augmented</em> Shallow Water Equations system for open channels and rivers with arbitrarily shaped cross sections, suitable for numerical integration when discontinuous geometry is encountered. The additional variable considered can be the bottom elevation, a reference width, a shape coefficient, or a vector containing these or other geometric parameters. The appropriate numerical method, which is well suited to coupling with the mathematical one, is a path-conservative method, capable of reconstructing the behaviour of physical and geometrical variables at the cell boundaries, where the discrete solution of hyperbolic systems of equations is discontinuous. A nonlinear path suitable for the shallow water context is adopted. The resulting model is shown to be well-balanced and accurate to the second order and is further validated against analytical solutions related to channels with power-law cross-sections, specifically for dam break patterns over a variable-width channel and the run-up dynamics of long water waves over sloping bays.</p></div>","PeriodicalId":7614,"journal":{"name":"Advances in Water Resources","volume":"189 ","pages":"Article 104735"},"PeriodicalIF":4.0000,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0309170824001222/pdfft?md5=81c602771578d2080bf566afd0027f66&pid=1-s2.0-S0309170824001222-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A one-dimensional augmented Shallow Water Equations system for channels of arbitrary cross-section\",\"authors\":\"A. Valiani, V. Caleffi\",\"doi\":\"10.1016/j.advwatres.2024.104735\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This work provides a new formulation of the one-dimensional <em>augmented</em> Shallow Water Equations system for open channels and rivers with arbitrarily shaped cross sections, suitable for numerical integration when discontinuous geometry is encountered. The additional variable considered can be the bottom elevation, a reference width, a shape coefficient, or a vector containing these or other geometric parameters. The appropriate numerical method, which is well suited to coupling with the mathematical one, is a path-conservative method, capable of reconstructing the behaviour of physical and geometrical variables at the cell boundaries, where the discrete solution of hyperbolic systems of equations is discontinuous. A nonlinear path suitable for the shallow water context is adopted. The resulting model is shown to be well-balanced and accurate to the second order and is further validated against analytical solutions related to channels with power-law cross-sections, specifically for dam break patterns over a variable-width channel and the run-up dynamics of long water waves over sloping bays.</p></div>\",\"PeriodicalId\":7614,\"journal\":{\"name\":\"Advances in Water Resources\",\"volume\":\"189 \",\"pages\":\"Article 104735\"},\"PeriodicalIF\":4.0000,\"publicationDate\":\"2024-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0309170824001222/pdfft?md5=81c602771578d2080bf566afd0027f66&pid=1-s2.0-S0309170824001222-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Water Resources\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0309170824001222\",\"RegionNum\":2,\"RegionCategory\":\"环境科学与生态学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"WATER RESOURCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Water Resources","FirstCategoryId":"93","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0309170824001222","RegionNum":2,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"WATER RESOURCES","Score":null,"Total":0}
A one-dimensional augmented Shallow Water Equations system for channels of arbitrary cross-section
This work provides a new formulation of the one-dimensional augmented Shallow Water Equations system for open channels and rivers with arbitrarily shaped cross sections, suitable for numerical integration when discontinuous geometry is encountered. The additional variable considered can be the bottom elevation, a reference width, a shape coefficient, or a vector containing these or other geometric parameters. The appropriate numerical method, which is well suited to coupling with the mathematical one, is a path-conservative method, capable of reconstructing the behaviour of physical and geometrical variables at the cell boundaries, where the discrete solution of hyperbolic systems of equations is discontinuous. A nonlinear path suitable for the shallow water context is adopted. The resulting model is shown to be well-balanced and accurate to the second order and is further validated against analytical solutions related to channels with power-law cross-sections, specifically for dam break patterns over a variable-width channel and the run-up dynamics of long water waves over sloping bays.
期刊介绍:
Advances in Water Resources provides a forum for the presentation of fundamental scientific advances in the understanding of water resources systems. The scope of Advances in Water Resources includes any combination of theoretical, computational, and experimental approaches used to advance fundamental understanding of surface or subsurface water resources systems or the interaction of these systems with the atmosphere, geosphere, biosphere, and human societies. Manuscripts involving case studies that do not attempt to reach broader conclusions, research on engineering design, applied hydraulics, or water quality and treatment, as well as applications of existing knowledge that do not advance fundamental understanding of hydrological processes, are not appropriate for Advances in Water Resources.
Examples of appropriate topical areas that will be considered include the following:
• Surface and subsurface hydrology
• Hydrometeorology
• Environmental fluid dynamics
• Ecohydrology and ecohydrodynamics
• Multiphase transport phenomena in porous media
• Fluid flow and species transport and reaction processes