An adaptive mesh rezoning scheme for moving boundary flows and fluid–structure interaction. (English) Zbl 1181.76108

Summary: Arbitrary Lagrangian–Eulerian (ALE) techniques provide a general framework for solving moving boundary flows and fluid–structure interaction problems. ALE formulations allow freedom of prescribing the fluid mesh velocity which can be independent of the velocity of the fluid particles. A major challenge in ALE descriptions lies in developing mesh moving techniques to update the fluid mesh and map the moving domain in a rational way. Exploiting the notion of arbitrary mesh velocity for the fluid domain, we have developed an adaptive mesh rezoning technique for structured and unstructured meshes. The method has been applied to meshes composed of triangles, quadrilaterals, as well as an arbitrary combination of these two element types in the computational domain. This feature of the proposed scheme is very attractive from practical problem solving viewpoint in that it allows kinematically complex problems to be handled effectively. A variety of test cases are shown that involve single and/or multiple moving objects. Embedding the mesh rezoning scheme in our flow solver, we also present some representative simulations of flows over moving meshes.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76T99 Multiphase and multicomponent flows
Full Text: DOI


[1] Aquelet, N.; Souli, M.; Olovsson, L., Euler – lagrange coupling with damping effects: application to slamming problems, Comput meth appl mech eng, 29, 329-349, (1984) · Zbl 1137.74430
[2] Babuska, I., Error bounds for finite element method, Numer math, 16, 322-333, (1971) · Zbl 0214.42001
[3] Barbosa, H.J.C.; Hughes, T.J.R., The finite element method with Lagrange multipliers on the boundary: circumventing the babuska – brezzi condition, Comput meth appl mech eng, 85, 1, 109-128, (1991) · Zbl 0764.73077
[4] Belytschko, T.; Kennedy, J.M.; Schoeberie, D.F., Quasi-Eulerian finite element formulation for fluid – structure interaction, ASME J press vess technol, 102, 62-69, (1980)
[5] Bottasso, C.L.; Detomi, D.; Serra, R., The ball-vertex method: a new simple spring analogy method for unstructured dynamic meshes, Comput meth appl mech eng, 194, 39-41, 4244-4264, (2005) · Zbl 1151.74429
[6] Brackbill, J.U.; Saltzman, J.S., Adaptive zoning for singular problems in two dimensions, J comput phys, 46, 342-368, (1982) · Zbl 0489.76007
[7] Brezzi, F.; Fortin, M., Mixed and hybrid finite element methods, (1991), Springer-Verlag New York-Heidelberg-Berlin · Zbl 0788.73002
[8] Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, Rev fr automat inform recher oper. ser rouge anal numer, R-2, 129-151, (1974) · Zbl 0338.90047
[9] Chen JS, Liu WK, Belytschko T. Arbitrary Lagrangian-Eulerian methods for materials with memory and friction. In: Tezduyar TE, Hughes TJR, editors. Recent developments in computational fluid dynamics, AMD-vol. 95. 1988.
[10] Ciarlet, P.G., The finite element method for elliptic problems, (1978), North-Holland Amsterdam · Zbl 0445.73043
[11] Degand, C.; Farhat, C., A three-dimensional torsional spring analogy method for unstructured dynamic meshes, Comput struct, 80, 305-316, (2002)
[12] Donea, J., Arbitrary lagrangian – eulerian finite element methods, (), 473-516
[13] Donea J, Fasoli-Stella P, Giuliani S. Lagrangian and Eulerian finite element techniques for transient fluid – structure interaction problems. In: Transactions of the 4th international conference on structural mechanics in reactor technology, Paper B1/2. 1977.
[14] Farhat, C.; Degand, C.; Koobus, B.; Lesoinne, M., Torsional springs for two-dimensional dynamic unstructured fluid meshes, Comput meth appl mech eng, 163, 231-245, (1998) · Zbl 0961.76070
[15] Farhat, C.; Pierson, K.; Degand, C., Multidisciplinary simulation of the maneuvering of an aircraft, Eng comput, 17, 16-27, (2001) · Zbl 1002.68531
[16] R.M. Ferencz, Element-by-element preconditioning techniques for large-scale, vectorized finite element analysis in nonlinear solid and structural mechanics. Ph.D. Thesis, Division of Applied Mechanics, Stanford University, 1989.
[17] Godunov, S.K.; Prokopov, G.P., The use of moving meshes in gas-dynamic calculations, USSR comput math math phys, 12, 2, 182-191, (1972) · Zbl 0271.76057
[18] Glowinski, R.; Tallec, P.L., Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM studies in applied mathematics, (1989), Society for Industrial and Applied Mathematics Philadelphia, Pennsylvania · Zbl 0698.73001
[19] Hassan, O.; Probert, E.J.; Morgan, K.; Weatherill, N.P., Unsteady flow simulation using unstructured meshes, Comput meth appl mech eng, 189, 1247-1275, (2000) · Zbl 0992.76054
[20] Hughes, T.J.R.; Liu, W.K.; Zimmerman, T.K., Lagrangian – eulerian finite element formulation for incompressible viscous flows, Comput meth appl mech eng, 29, 329-349, (1984)
[21] Hughes, T.J.R.; Mallet, M., A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective – diffusive systems, Comput meth appl mech eng, 58, 329-339, (1986) · Zbl 0587.76120
[22] Johnson, A.A.; Tezduyar, T.E., Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Comput meth appl mech eng, 119, 73-94, (1994) · Zbl 0848.76036
[23] Johnson, A.A.; Tezduyar, T.E., Simulation of multiple spheres falling in a liquid-filled tube, Comput meth appl mech eng, 134, 351-373, (1996) · Zbl 0895.76046
[24] Johnson, A.A.; Tezduyar, T.E., Advanced mesh generation and update methods for 3D flow simulations, Comput mech, 23, 130-143, (1999) · Zbl 0949.76049
[25] Koobus, B.; Farhat, C., Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes, Comput meth appl mech eng, 170, 103-129, (1999) · Zbl 0943.76055
[26] Masud A. On a stabilized formulation for incompressible Navier-Stokes equations. In: Kanayama H, editor. Proc 6th Japan-US international symposium on flow simulation and modeling, Fukuoka, Japan. May 2002, p. 33-8.
[27] Masud, A.; Hughes, T.J.R., A space – time Galerkin/least-squares finite element formulation of the navier – stokes equations for moving domain problems, Comput meth appl mech eng, 146, 91-126, (1997) · Zbl 0899.76259
[28] Masud A, Khurram RA. A multiscale finite element method for the incompressible Navier-Stokes equation, Comput Meth Appl Mech Eng, in press. · Zbl 1178.76233
[29] Masud A, Khurram R, Bhagwanwala M, A stable method for fluid – structure interaction problems. In: Yao ZH, Yuan MW, Zhong WX, editors. Proceedings CD-ROM of the sixth world congress on computational mechanics. ISBN 7-89494-512-9, Beijing, China, 2004.
[30] Mittal, S.; Aliabadi, S.; Tezduyar, T., Parallel computation of unsteady compressible flows with the EDICT, Comput mech, 23, 151-157, (1999) · Zbl 0951.76045
[31] Mittal, S.; Tezduyar, T.E., A finite element study of incompressible flows past oscillating cylinders and airfoils, Int J numer meth fluids, 15, 1073-1118, (1992)
[32] Lesoinne, M.; Farhat, C., Geometric conservation laws for flow problems boundaries and deformable meshes, and their aeroelastic computations, Comput meth appl mech eng, 134, 71-90, (1996) · Zbl 0896.76044
[33] Nkonga, B., On the conservative and accurate CFD approximations for moving meshes and moving boundaries, Comput meth appl mech eng, 190, 1801-1825, (2000) · Zbl 1010.76063
[34] Stein, K.; Tezduyar, T.; Benney, R., Mesh moving techniques for fluid – structure interactions with large displacements, J appl mech, 70, 58-63, (2003) · Zbl 1110.74689
[35] Stein, K.; Tezduyar, T.E.; Benney, R., Automatic mesh update with the solid-extension mesh moving technique, Comput meth appl mech eng, 193, 2019-2032, (2004) · Zbl 1067.74587
[36] Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Kalro, V.; Litke, M., Flow simulation and high performance computing, Comput mech, 18, 397-412, (1996) · Zbl 0893.76046
[37] Tezduyar, T.E.; Behr, M.; Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space – time procedure: I. the concept and the preliminary tests, Comput meth appl mech eng, 94, 339-351, (1992) · Zbl 0745.76044
[38] Tezduyar, T.E.; Behr, M.; Mittal, S.; Johnson, A.A., Computation of unsteady incompressible flows with the stabilized finite element methods—space – time formulations, iterative strategies and massively parallel implementations, New methods in transient analysis, PVP-vol. 246/AMD-vol. 143, (1992), ASME New York, p. 7-24
[39] Wang, H.P.; McLay, R.T., Automatic remeshing scheme for modeling hot forming process, J fluid eng, 108, 465-469, (1986)
[40] Winslow AM. Equipotential zoning of two-dimensional meshes. University of California, Lawrence Radiation Laboratory Report, UCRL-7312, 1963.
[41] Zhao, Y.; Forhad, A., A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids, Comput meth appl mech eng, 192, 4439-4466, (2003) · Zbl 1054.76541
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.