Startseite Numerical Analysis of a Finite Element Approximation to a Level Set Model for Free-Surface Flows
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Numerical Analysis of a Finite Element Approximation to a Level Set Model for Free-Surface Flows

  • Tomás Chacón Rebollo ORCID logo EMAIL logo , Macarena Gómez Mármol ORCID logo und Isabel Sánchez Muñoz ORCID logo
Veröffentlicht/Copyright: 8. September 2021

Abstract

In this paper, we study a finite element discretization of a Level Set Method formulation of free-surface flow. We consider an Euler semi-implicit discretization in time and a Galerkin discretization of the level set function. We regularize the density and viscosity of the flow across the interface, following the Level Set Method. We prove stability in natural norms when the viscosity and density vary from one to the other layer and optimal error estimates for smooth solutions when the layers have the same density. We present some numerical tests for academic flows.

MSC 2010: 76T10; 65M12; 65M22

Award Identifier / Grant number: RTI2018-093521-B-C31

Award Identifier / Grant number: US-125487

Funding statement: Research partially supported by the Spanish Research Agency (AEI) and European Union FEDER project RTI2018-093521-B-C31 and by Programa Operativo FEDER Andalucía 2014–2020 Project US-125487.

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Received: 2021-03-15
Revised: 2021-08-04
Accepted: 2021-08-10
Published Online: 2021-09-08
Published in Print: 2022-01-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 18.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/cmam-2021-0052/html
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