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Numerical simulation of unsteady viscous free surface flow. (English) Zbl 0701.76036
Summary: A finite element method is presented for the numerical simulation of time-dependent incompressible viscous free surface flows. The time- dependent primitive equations are solved sequentially using explicit time marching procedure. The method is based on a velocity correction approach to the time integration of the Navier-Stokes equations in which only the incompressibility condition is treated implicitly. A special arbitrary mixed Lagrangian-Eulerian description has been used to avoid the typical problems encountered in a purely Lagrangian description. The method appears applicable for small computers; problems requiring several thousand nodes can be solved on personal computers. Numerical experiments have been performed that show that this approach is reasonably efficient and robust for a range of complicated highly nonlinear problems.

76D05 Navier-Stokes equations for incompressible viscous fluids
76M10 Finite element methods applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D33 Waves for incompressible viscous fluids
Full Text: DOI
[1] Nickell, R.E.; Tanner, R.I.; Caswell, B., J. fluid. mech., 65, 189, (1974)
[2] Reddy, K.R.; Tanner, R.I., Comput. fluids, 6, 83, (1978)
[3] Orr, F.M.; Scriven, L.E., J. fluid. mech., 84, 145, (1978)
[4] Silliman, W.J.; Scriven, L.E., J. comput. phys., 34, 287, (1980)
[5] Ruschak, K.J., Int. J. num. methods eng., 15, 639, (1980)
[6] Kheshgi, H.S.; Scriven, L.E., (), 113
[7] Dupret, F., (), 495
[8] Wellford, L.C.; Ganaba, T.H., Int. J. num. methods eng., 17, 1201, (1981)
[9] Frederiksen, C.S.; Watts, A.M., J. comput. phys., 39, 282, (1981)
[10] Kawahara, M.; Miwa, T., Int. J. num. methods eng., 20, 1193, (1984)
[11] Bach, P.; Hassager, O., J. fluid. mech., 152, 173, (1985)
[12] Ramaswamy, B.; Kawahara, M.; Nakayama, T., Int. J. num. methods fluids, 6, 659, (1986)
[13] Ramaswamy, B.; Kawahara, M., Int. J. num. methods fluids, 7, 953, (1987)
[14] Hirt, C.W.; Amsden, A.A.; Cook, J.L., J. comput. phys., 14, 227, (1974)
[15] Laitone, E.V., J. fluid. mech., 9, 430, (1960)
[16] Grimshaw, R., J. fluid. mech., 46, 611, (1971)
[17] Fenton, J., J. fluid. mech., 53, 257, (1972)
[18] Harlow, F.H.; Welch, J.E., Phys. fluids, 8, 2182, (1965)
[19] Amsden, A.A.; Harlow, F.H., J. comput. phys., 6, 322, (1970)
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