# 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 Bermejo Bermejo, Rodolfo Prieto Ortiz, Juan Luis Article Siam Journal on Scientific Computing 2013 1064-8275 35 Level set, semi-Lagrangian, reinitialization, finite elements, incompressible flows,interfaces. E.T.S.I. Industriales (UPM) Matemática Aplicada a la Ingeniería Industrial 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.

Item ID: 29481 http://oa.upm.es/29481/ oai:oa.upm.es:29481 10.1137/110830587 http://epubs.siam.org/doi/abs/10.1137/110830587 Memoria Investigacion 31 Oct 2014 16:55 31 Oct 2014 16:55

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