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


Autoria(s): Bermejo Bermejo, Rodolfo; Prieto Ortiz, Juan Luis
Data(s)

2013

Resumo

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.

Formato

application/pdf

Identificador

http://oa.upm.es/29481/

Idioma(s)

eng

Publicador

E.T.S.I. Industriales (UPM)

Relação

http://oa.upm.es/29481/1/INVE_MEM_2013_160658.pdf

http://epubs.siam.org/doi/abs/10.1137/110830587

info:eu-repo/semantics/altIdentifier/doi/10.1137/110830587

Direitos

http://creativecommons.org/licenses/by-nc-nd/3.0/es/

info:eu-repo/semantics/openAccess

Fonte

Siam Journal on Scientific Computing, ISSN 1064-8275, 2013, Vol. 35, No. 4

Palavras-Chave #Matemáticas
Tipo

info:eu-repo/semantics/article

Artículo

PeerReviewed