A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

Bermejo Bermejo, Rodolfo and Prieto Ortiz, Juan Luis (2013). A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems. "Siam Journal on Scientific Computing", v. 35 (n. 4); pp.. ISSN 1064-8275. https://doi.org/10.1137/110830587.

Description

Title: A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems
Author/s:
  • Bermejo Bermejo, Rodolfo
  • Prieto Ortiz, Juan Luis
Item Type: Article
Título de Revista/Publicación: Siam Journal on Scientific Computing
Date: 2013
ISSN: 1064-8275
Volume: 35
Subjects:
Freetext Keywords: Level set, semi-Lagrangian, reinitialization, finite elements, incompressible flows,interfaces.
Faculty: E.T.S.I. Industriales (UPM)
Department: Matemática Aplicada a la Ingeniería Industrial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semi-Lagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm, � · �h,∞, and the error analysis shows that when the level set solution u(t) is in the Sobolev space Wr+1,∞(D), r ≥ 0, the convergence in the maximum norm is of the form (KT/Δt)min(1,Δt � v �h,∞ /h)((1 − α)hp + hq), p = min(2, r + 1), and q = min(3, r + 1),where v is a velocity. This means that at high CFL numbers, that is, when Δt > h, the error is O( (1−α)hp+hq) Δt ), whereas at CFL numbers less than 1, the error is O((1 − α)hp−1 + hq−1)). We have tested our method with satisfactory results in benchmark problems such as the Zalesak’s slotted disk, the single vortex flow, and the rising bubble.

More information

Item ID: 29481
DC Identifier: http://oa.upm.es/29481/
OAI Identifier: oai:oa.upm.es:29481
DOI: 10.1137/110830587
Official URL: http://epubs.siam.org/doi/abs/10.1137/110830587
Deposited by: Memoria Investigacion
Deposited on: 31 Oct 2014 16:55
Last Modified: 31 Oct 2014 16:55
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