Numerical Analysis of a Finite Element Approximation to a Level Set Model for Free-Surface Flows-Reference-Cited by-同舟云学术

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

Published:2021-09-08 Issue:1 Volume:22 Page:155-179
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Chacón Rebollo Tomás¹^ORCID,Gómez Mármol Macarena²^ORCID,Sánchez Muñoz Isabel³^ORCID

Affiliation:

1. Departamento EDAN & IMUS , Facultad de Matemáticas, Campus de Reina Mercedes , Universidad de Sevilla , 41927 Sevilla , Spain

2. Departamento EDAN , Facultad de Matemáticas, Campus de Reina Mercedes , Universidad de Sevilla , 41927 Sevilla , Spain

3. Departamento Matemática Aplicada I , E.T.S. de Ingeniería Agronómica , Universidad de Sevilla , Ctra. Utrera, Km 1, 41013 Sevilla , Spain

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2021-0052/pdf

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