zbMATH — the first resource for mathematics

Parallel finite element simulation of 3D incompressible flows: Fluid-structure interactions. (English) Zbl 0873.76047
The authors present numerical results for unsteady incompressible three-dimensional flows, including those with fluid-structure interactions. These computations in time-varying spatial domains are carried out on the AHPCRC supercomputers CM-200 and CM-5 with provision for major speed-ups compared with traditional supercomputers, based on the massively parallel implementations of the deforming spatial domain and on stabilized space-time finite element formulations.
The capability to solve three-dimensional problems involving fluid-structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Good agreement with observations by other researchers is obtained. Computations of flow past a stationary rectangular wing confirm the presence of wing tip vortices. An interesting pattern of vortex shedding is observed at Reynolds number 2500. In these computations, at each time step, approximately \(3\times 10^6\) nonlinear equations are solved to update the flow field.
Preliminary results are presented for flow past a wing in flapping motion based on description of the flight of birds given by J. Lighthill [An informal introduction to theoretical fluid mechanics. Oxford: Clarendon Press (1986; Zbl 0604.76002)]. The use of a specially designed mesh-moving scheme in conjunction with the stabilized space-time formulation eliminates the need for remeshing, ensures high accuracy of solutions, and aids in the efficient utilization of the massively parallel computers.

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65Y05 Parallel numerical computation
Full Text: DOI
[1] Tezduyar, Comput. Methods Appl. Mech. Eng. 94 pp 339– (1992)
[2] Tezduyar, Comput. Methods Appl. Mech. Eng. 94 pp 353– (1992)
[3] Mittal, Int. j. numer. methods fluids 15 pp 1073– (1992)
[4] Mittal, Comput. Methods Appl. Mech. Eng. 112 pp 253– (1994)
[5] Behr, Comput. Methods Appl. Mech. Eng. 108 pp 99– (1993)
[6] Saad, SIAM J. Sci. Stat. Comput. 7 pp 856– (1986)
[7] Kennedy, Comput. Methods Appl. Mech. Eng. 119 pp 95– (1994)
[8] Housner, J. Appl. Mech. 19 pp 205– (1952)
[9] Gregory, Proc. R. Soc. Lond. A 293 pp 512– (1966)
[10] Gregory, Proc. R. Soc. Lond. A 293 pp 528– (1966)
[11] Benjamin, Proc. R. Soc. Lond. A 261 pp 457– (1961)
[12] Benjamin, Proc. R. Soc. Lond. A 261 pp 487– (1961)
[13] Paidoussis, J. Sound Vibr. 33 pp 267– (1974)
[14] Hilber, Earthq. Eng. Struct. Dyn. 5 pp 283– (1977)
[15] An Informatl Introduction to Theoretical Fluid Mechanics, Clarendon, Oxford, 1986.
[16] Tezduyar, Comput. Methods Appl. Mech. Eng. 95 pp 221– (1992)
[17] Boundary Layer Theory, transl. by J. Kestin, McGraw-Hill, New York, 1968.
[18] Johnson, Comput. Methods Appl. Mech. Eng. 119 pp 73– (1994)
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.