The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Nonlinear Simulation of Transient Free Surface Flows
Nonlinear Simulation of Transient Free Surface Flows
Pages 239-250
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From page 239... ...
2 Introduction The direct numerical simulation of unsteady two-dimensional potential free surface flows using a Mixed EulerianLagrangian method (MEL) has received considerable attention since the pioneering work of Longuet-Higgins and Cokelet t224.
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This allows an analytical integration of the Green function, its normal derivative and their products by the curvilinear abscissa so that the calculation of the matrix elements is rather simple (and vectorizes well)
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In practice, the damping coefficient Waxy is equal to zero except in the damping zone (x > no) ' is chosen continuous and continuously differentiable, and is "tuned" to a characteristic wave frequency ~ and to a characteristic wave number k: waxy = <~w t2 x _ pJ2, x > To = 13.
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In any event, a comparison with a linear result appears necessary in order to be sure that nonlinear phenomena are important. It should also be kept in mind that viscous effects can play an important role and are not accounted for in the simulation so that discrepancies might not be due to the inaccuracy of the numerical scheme but to an improper physical modeling.
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This is very likely due to the numerical treatment at the intersection that is not second-order4. 4.2.2 Linear Solution in a Tank of Infinite Length In order to test the efficiency of the damping zone, we consider now a tank of infinite length.
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From page 244... ...
If long-lasting low frequency oscillations appear, the relative error is only of a few percents and the absorption mechanism appears to be quite satisfactory. 4.2.3 Nonlinear Solution in Shallow Water In order to estimate the accuracy of the method for the nonlinear computation, we first consider the case of a shallow water swell.
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6. This confirms that the numerical simulation can reproduce accurately nonlinear phenomena observed experimentaly.
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performed experiments related to incoming deepwater Stokes waves passing over a restrained submerged circular cylinder. For a small cylinder submer gence, a strong local nonlinearity is introduced at the free surface above the cylinder and free higher order harmonic waves are generated.
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Here again, the validity of the simulation is difficult to establish. It is rather interesting to note that for waves passing over a submerged cylinder, nonlinear free surface effects are important for the diffracted waves but do not seem to affect very much the forces.
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x ~ ' it/ f rr _/ f ~~ an-, Figure 15: Forced heaving free surface profiles The second term on the left-hand side is the linear hydrostatic contribution. The acceleration-phase and velocityphase components of the force at the forcing frequency would correspond to the added mass and damping coefficients for the linear problems.
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Results have been presented that include a wide range of applications, such as wave generation and absorption, wave diffraction and wave radiation by submerged or surface piercing bodies in forced or free motion. Results from approximate theories (linear, second-order or shallow water theory)
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[17] GRUE, J., and GRANLUND, K., 1988, "Impact of nonlinearity upon waves traveling over a submerged cylinder," Third International Workshop on Water Waves and Floating Bodies (Woods Hole)
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