×

An immersed smoothed finite element method for fluid–structure interaction problems. (English) Zbl 1245.74012

Summary: A novel procedure, immersed smoothed finite element method (immersed S-FEM) is proposed for solving fluid-structure interaction (FSI) problems with moving nonlinear solids, using triangular type of mesh. The method consists of well-combined three ingredients: two-step Taylor-characteristic-based-Galerkin (TCBG) method for incompressible viscous Navier-Stokes flows, the S-FEM for explicit dynamics analysis of nonlinear solids and structures, and FSI conditions using immersed technique with a modified direct force evaluation technique. Such a combination is designed for ensuring stability, best possible efficiency, and simplicity and convenient to use. The proposed method is verified by numerical examples using triangular meshes, which demonstrate the validity, accuracy, and the second-order convergence properties of the present method in both space and time.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76M10 Finite element methods applied to problems in fluid mechanics
74S05 Finite element methods applied to problems in solid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bao Y., Int. J. Numer. Meth. Fluids 62 pp 1181–
[2] Belytschko T., Nonlinear Finite Elements for Continua and Structures (2000) · Zbl 0959.74001
[3] DOI: 10.1016/0045-7825(82)90071-8 · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[4] DOI: 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A · Zbl 1011.74081 · doi:10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
[5] DOI: 10.1006/jcph.2000.6484 · Zbl 0972.76073 · doi:10.1006/jcph.2000.6484
[6] DOI: 10.1016/0045-7825(94)90022-1 · Zbl 0845.76069 · doi:10.1016/0045-7825(94)90022-1
[7] DOI: 10.1201/9781420082104 · Zbl 1205.74003 · doi:10.1201/9781420082104
[8] DOI: 10.1016/j.jsv.2008.08.027 · doi:10.1016/j.jsv.2008.08.027
[9] Liu G. R., Int. J. Numer. Meth. Eng. 81 pp 1093–
[10] Liu G. R., Int. J. Numer. Meth. Eng. 81 pp 1127–
[11] DOI: 10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X · Zbl 1050.74057 · doi:10.1002/1097-0207(20010210)50:4<937::AID-NME62>3.0.CO;2-X
[12] DOI: 10.1201/EBK1439820278 · doi:10.1201/EBK1439820278
[13] DOI: 10.1016/0021-9991(77)90100-0 · Zbl 0403.76100 · doi:10.1016/0021-9991(77)90100-0
[14] DOI: 10.1002/nme.608 · Zbl 1032.76037 · doi:10.1002/nme.608
[15] DOI: 10.1007/s00466-009-0449-5 · Zbl 1362.74035 · doi:10.1007/s00466-009-0449-5
[16] DOI: 10.1016/j.cma.2003.12.044 · Zbl 1067.76576 · doi:10.1016/j.cma.2003.12.044
[17] DOI: 10.1002/nme.3049 · Zbl 1235.74328 · doi:10.1002/nme.3049
[18] DOI: 10.1002/(SICI)1097-0363(19990915)31:1<359::AID-FLD984>3.0.CO;2-7 · Zbl 0985.76069 · doi:10.1002/(SICI)1097-0363(19990915)31:1<359::AID-FLD984>3.0.CO;2-7
[19] Zienkiewicz O. C., Fluid Dynamics 3, in: The Finite Element Method (2000) · Zbl 0991.74004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.