{"title":"不可压缩流动的半拉格朗日有限元外部微积分","authors":"Wouter Tonnon, Ralf Hiptmair","doi":"10.1007/s10444-023-10092-6","DOIUrl":null,"url":null,"abstract":"<p>We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary simplicial meshes. We recast the equations as a nonlinear transport problem for a momentum 1-form and discretize in space using methods from finite element exterior calculus. Numerical experiments show that the linearly implicit fully discrete version of the scheme enjoys excellent stability properties in the vanishing viscosity limit and is applicable to inviscid incompressible Euler flows. We obtain second-order convergence and conservation of energy is achieved through a Lagrange multiplier.</p>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semi-Lagrangian finite element exterior calculus for incompressible flows\",\"authors\":\"Wouter Tonnon, Ralf Hiptmair\",\"doi\":\"10.1007/s10444-023-10092-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary simplicial meshes. We recast the equations as a nonlinear transport problem for a momentum 1-form and discretize in space using methods from finite element exterior calculus. Numerical experiments show that the linearly implicit fully discrete version of the scheme enjoys excellent stability properties in the vanishing viscosity limit and is applicable to inviscid incompressible Euler flows. We obtain second-order convergence and conservation of energy is achieved through a Lagrange multiplier.</p>\",\"PeriodicalId\":50869,\"journal\":{\"name\":\"Advances in Computational Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-02-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Computational Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10444-023-10092-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10444-023-10092-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Semi-Lagrangian finite element exterior calculus for incompressible flows
We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary simplicial meshes. We recast the equations as a nonlinear transport problem for a momentum 1-form and discretize in space using methods from finite element exterior calculus. Numerical experiments show that the linearly implicit fully discrete version of the scheme enjoys excellent stability properties in the vanishing viscosity limit and is applicable to inviscid incompressible Euler flows. We obtain second-order convergence and conservation of energy is achieved through a Lagrange multiplier.
期刊介绍:
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.