{"title":"潮湿浅水方程的兼容有限元离散化","authors":"Nell Hartney, Thomas M. Bendall, Jemma Shipton","doi":"arxiv-2409.07182","DOIUrl":null,"url":null,"abstract":"The moist shallow water equations offer a promising route for advancing\nunderstanding of the coupling of physical parametrisations and dynamics in\nnumerical atmospheric models, an issue known as 'physics-dynamics coupling'.\nWithout moist physics, the traditional shallow water equations are a simplified\nform of the atmospheric equations of motion and so are computationally cheap,\nbut retain many relevant dynamical features of the atmosphere. Introducing\nphysics into the shallow water model in the form of moisture provides a tool to\nexperiment with numerical techniques for physics-dynamics coupling in a simple\ndynamical model. In this paper, we compare some of the different moist shallow\nwater models by writing them in a general formulation. The general formulation\nencompasses three existing forms of the moist shallow water equations and also\na fourth, previously unexplored formulation. The equations are coupled to a\nthree-state moist physics scheme that interacts with the resolved flow through\nsource terms and produces two-way physics-dynamics feedback. We present a new\ncompatible finite element discretisation of the equations and apply it to the\ndifferent formulations of the moist shallow water equations in three test\ncases. The results show that the models capture generation of cloud and rain\nand physics-dynamics interactions, and demonstrate some differences between\nmoist shallow water formulations and the implications of these different\nmodelling choices.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A compatible finite element discretisation for moist shallow water equations\",\"authors\":\"Nell Hartney, Thomas M. Bendall, Jemma Shipton\",\"doi\":\"arxiv-2409.07182\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The moist shallow water equations offer a promising route for advancing\\nunderstanding of the coupling of physical parametrisations and dynamics in\\nnumerical atmospheric models, an issue known as 'physics-dynamics coupling'.\\nWithout moist physics, the traditional shallow water equations are a simplified\\nform of the atmospheric equations of motion and so are computationally cheap,\\nbut retain many relevant dynamical features of the atmosphere. Introducing\\nphysics into the shallow water model in the form of moisture provides a tool to\\nexperiment with numerical techniques for physics-dynamics coupling in a simple\\ndynamical model. In this paper, we compare some of the different moist shallow\\nwater models by writing them in a general formulation. The general formulation\\nencompasses three existing forms of the moist shallow water equations and also\\na fourth, previously unexplored formulation. The equations are coupled to a\\nthree-state moist physics scheme that interacts with the resolved flow through\\nsource terms and produces two-way physics-dynamics feedback. We present a new\\ncompatible finite element discretisation of the equations and apply it to the\\ndifferent formulations of the moist shallow water equations in three test\\ncases. The results show that the models capture generation of cloud and rain\\nand physics-dynamics interactions, and demonstrate some differences between\\nmoist shallow water formulations and the implications of these different\\nmodelling choices.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.07182\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07182","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A compatible finite element discretisation for moist shallow water equations
The moist shallow water equations offer a promising route for advancing
understanding of the coupling of physical parametrisations and dynamics in
numerical atmospheric models, an issue known as 'physics-dynamics coupling'.
Without moist physics, the traditional shallow water equations are a simplified
form of the atmospheric equations of motion and so are computationally cheap,
but retain many relevant dynamical features of the atmosphere. Introducing
physics into the shallow water model in the form of moisture provides a tool to
experiment with numerical techniques for physics-dynamics coupling in a simple
dynamical model. In this paper, we compare some of the different moist shallow
water models by writing them in a general formulation. The general formulation
encompasses three existing forms of the moist shallow water equations and also
a fourth, previously unexplored formulation. The equations are coupled to a
three-state moist physics scheme that interacts with the resolved flow through
source terms and produces two-way physics-dynamics feedback. We present a new
compatible finite element discretisation of the equations and apply it to the
different formulations of the moist shallow water equations in three test
cases. The results show that the models capture generation of cloud and rain
and physics-dynamics interactions, and demonstrate some differences between
moist shallow water formulations and the implications of these different
modelling choices.