Calculation of transient motion of submerged cables
Authors: Thomas S. Walton and Harry Polachek
Journal: Math. Comp. 14 (1960), 27-46
MSC: Primary 65.00
MathSciNet review: 0116470
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Abstract: The system of nonlinear partial differential equations governing the transient motion of a cable immersed in a fluid is solved by finite difference methods. This problem may be considered a generalization of the classical vibrating string problem in the following respects: a) the motion is two dimensional, b) large displacements are permitted, c) forces due to the weight of the cable, buoyancy, drag and virtual inertia of the medium are included, and d) the properties of the cable need not be uniform. The numerical solution of this system of equations presents a number of interesting mathematical problems related to: a) the nonlinear nature of the equations, b) the determination of a stable numerical procedure, and c) the determination of an effective computational method. The solution of this problem is of practical significance in the calculation of the transient forces acting on mooring and towing lines which are subjected to arbitrarily prescribed motions.
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-  G. Ludford, H. Polachek, and R. J. Seeger, On unsteady flow of compressible viscous fluids, J. Appl. Phys. 24 (1953), 490–495. MR 55126
- T. S. Walton & H. Polachek, ``Calculation of nonlinear transient motion of cables,'' David Taylor Model Basin Report 1279, 1959.
- G. G. O'Brien, M. A. Hyman & S. Kaplan, ``A study of the numerical solution of partial differential equations,'' Jn. Math. and Phys., v. 29, 1951, p. 223-251. MR 0040805 (12:751e)
- P. D. Lax & R. D. Richtmeyer, ``Stability of difference equations,'' Com. Pure Appl. Math., v. 9, 1956, p. 267-293. MR 0079204 (18:48c)
- G. Ludford, H. Polachek & R. J. Seeger, ``On unsteady flow of compressible viscous fluids,'' Jn. Appl. Phys., v. 24, 1953, p. 490-495. MR 0055126 (14:1032c)
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