A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems
Data(s) |
2013
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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 | |
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 |