“Finite Element Modelling of the Hydrodynamic Environment of a Small ROV”
Authors: Ren Guang and Jens G. Balchen,Affiliation: Dalian Maritime University (China) and NTNU, Department of Engineering Cybernetics
Reference: 1993, Vol 14, No 3, pp. 145-159.
Keywords: Moving boundary, finite element, hydrodynamic model, AUV
Abstract: This paper addresses a practical problem, namely, modeling the hydrodynamic environment of a small ROV. This has become the problem of solving time-dependent incompressible Navier-Stokes equations with moving boundaries and a new method is developed to solve it. Navier-Stokes equations expressed in a moving-body-fixed coordinate frame with moving boundaries are derived and solved by a proposed finite element method which is a modified velocity correction procedure (Ren and Utnes 1993). The present method is implemented in the C language on a SUN/Sparc Station. The algorithm and program are demonstrated by solving a classic driven cavity flow problem and a simplified model of the hydrodynamic environment of a small ROV, which is a moving boundary problem. The results from the driven cavity flow problem are compared to previous work. A definition is also given of the moving boundary problem (MBP) related to the solution of Navier-Stokes equations.
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DOI: 10.4173/mic.1993.3.3DOI forward links to this article:
| [1] H. Pan and M. Damodaran (2001), doi:10.2514/6.2001-2585 |
| [2] H. Pan and M. Damodaran (2002), doi:10.1002/fld.371 |
[1] CRAIG, J.J. (1989). Introduction to Robotics, Addison-Wesley Publishing Company.
[2] CRANK, J. (1984). Free and Moving Boundary Problems, Oxford University Press, London.
[3] CRISTI, R., PAPOULIAS, F.A., HEALEY, A.J., (1990). Adaptive sliding mode control of autonomous underwater vehicles in the dive plane, I.E.E.E.J. Oceanic Engineering, 15, 152-160 doi:10.1109/48.107143
[4] CRYER, C.W. (1978). The interrelation between moving boundary problems and free boundary problems, Moving Boundary Problems, D.G. Wilson, A.D. Solomon and P.T. Boggs (ed.) (Academic Press, New York).
[5] DEMIRDZIC, I. PERIC, M. (1990). Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries, Int. J. Numer. Methods Fluids, 10, 771-790 doi:10.1002/fld.1650100705
[6] FOSSEN, T.I. (1991). Nonlinear Modelling and Control of Underwater Vehicles, Dr. Ing thesis, Norwegian Institute of Technology, Trondheim, Norway.
[7] FOSSEN, T.I. BALCHEN, J.G. (1988). Modeling and non-linear self-tuning robust trajectory control of an autonomous underwater vehicle, Modeling, Identification and Control, 9, 165-177 doi:10.4173/mic.1988.4.1
[8] GHIA, U., GHIA, K.N. SHIN, C.T. (1982). High-Re solution for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48, 387-411 doi:10.1016/0021-9991(82)90058-4
[9] GOHEEN, K.R. JEFFERYS, R. (1990). Multivariable self-tuning autopilots for autonomous and remotely operated underwater vehicles, I.E.E.E.J. Oceanic Engineering, 15, 144-151 doi:10.1109/48.107142
[10] GRESHO, P.M., CHAN, S.T., LEE, R.L. UPSON, C.D. (1984). A modified finite element method for solving the time-dependent incompressible Navier-Stokes equations, Part 2: Applications. Int. J. Numer. Methods Fluid, 4, 619-640 doi:10.1002/fld.1650040703
[11] HARLOW, F.H. WELCH, J.E. (1965). Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, The Physics of Fluids, 8, 2182-2189 doi:10.1063/1.1761178
[12] HAYASHI, M. HATANAKA, K. KAWAHARA, M. (1991). Lagrangian finite element method for free surface Navier-Stokes flow using fraction step methods, Int. J. Numer. Methods Fluids, 13, 805-840 doi:10.1002/fld.1650130702
[13] KOVACS, A. KAWAHARA, M. (1991). A finite element scheme based on the velocity correction method for the solution of the time-dependent incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 13, 403-423 doi:10.1002/fld.1650130402
[14] OGAWA, S. ISHIGURO, T. (1987). A method for computing flow fields around moving bodies, J. Comput. Phys., 69, 49-68 doi:10.1016/0021-9991(87)90155-0
[15] PEDLOSKY, J. (1987). Geophysical Fluid Dynamics, Springer-Verlag, New York.
[16] PRANDTL, L. TIETJENS, O.G. (1934). Applied Hydro- and Aeromechanics, Dover, New York.
[17] RAMASWAMY, B. KAWAHARA, M. (1987). Lagrangian finite element analysis applied to viscous free surface fluid flow, Int. J. Numer. Methods Fluids, 7, 953-984 doi:10.1002/fld.1650070906
[18] REN, G. UTNES, T. (1993). A finite element solution of the time-dependent incompressible Navier-Stokes equations using a modified velocity correction method, Int. J. Numerical Methods in Fluids.to appear doi:10.1002/fld.1650170502
[19] SANI, R.L., GRESHO, P.M., LEE, R.L., GRIFFITHS, D.F. ENGELMAN, M. (1981). The cause and cure, ! of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations: Part 2. Int. J. Numer. Methods Fluids, 1, 171-204 doi:10.1002/fld.1650010206
[20] SILVESTRE, C., LEMOS, J.M., SEQUEIRA, M.M. SENTIEIRO, J.S. (1990). Modeling and adaptive control of a deepwater FSV, IFAC 11th Conf., pp. 124-129.
[21] TEZDUYAR, T.E. BEHR, M. LIOU, J. (1992). 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 numerical tests, Computer Methods in Applied Mechanics and Engineering, 94, 339-351 doi:10.1016/0045-7825(92)90059-S
[22] TRIANTAFYLLOU, M.S. GROSENBAUGH, M.A., (1991). Robust control for underwater vehicle systems with time delays, I.E.E.E. J. Oceanic Engineering, 16, 146-151 doi:10.1109/48.64894
[23] VIECELLI, J.A. (1971). A computing method for incompressible flows bounded by moving walls, J. Comput. Phys., 8, 119-143 doi:10.1016/0021-9991(71)90039-8
[24] YOERGER, D.R. SLOTINE J.-J.E. (1985). Robust trajectory control of underwater vehicles, I.E.E.E. J. Oceanic Engineering, 10, 462-470 doi:10.1109/JOE.1985.1145131
[25] YOERGER, D.R., NEWMAN, J. B. SLOTINE, J.-J.E. (1986). Supervisory control system for the JASON ROV, I.E.E.E. J. Oceanic Engineering, 11, 392-39 doi:10.1109/JOE.1986.1145191
[26] YUH, J. (1990). A neural net controller for underwater robotic vehicles, I.E.E.E. J. Oceanic Engineering, 15, 161-166 doi:10.1109/48.107144
[27] YUH, J. (1990). Modeling and control of underwater robotic vehicles, I.E.E.E. Transactions on Systems, Man, and Cybernetics, 20, 1475-1483 doi:10.1109/21.61218
[28] ZIENKIEWICZ, O.C. TAYLOR, R.L. (1991). The Finite Element Method, Volume 2.McGraw-Hill, London.
BibTeX:
@article{MIC-1993-3-3,
title={{Finite Element Modelling of the Hydrodynamic Environment of a Small ROV}},
author={Guang, Ren and Balchen, Jens G.},
journal={Modeling, Identification and Control},
volume={14},
number={3},
pages={145--159},
year={1993},
doi={10.4173/mic.1993.3.3},
publisher={Norwegian Society of Automatic Control}
};