Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Three-Dimensional, Unsteady Computations of Nonlinear Waves Caused by Underwater Disturbances
Three-Dimensional, Unsteady Computations of Nonlinear Waves Caused by Underwater Disturbances
Pages 417-426
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From page 417... ...
1 Nomenclature CD CL CM Cp D Dm Fr F M drag coefficient lift coefficient moment coefficient pressure coefficient diameter of spheroid local mesh size Froude number hydrodynamic force acting on body hydrodynamic moment acting on body submerged depth of disturbance h _ i;' ,k unit vectors L Ld p r S Sib Sf Sb Sf length ot mayor axis of spheroid desingularization distance 1~' factor of desingularization M moment acting on body Nb node number on spheroid Nit number of elements on spheroid in ~ direction Nb number of elements on spheroid in x direction Of node number on free surface Nf N,,f n node number on free surface in x direction node number on free surface in y direction outward normal of body surface into fluid pressure position vector from center of body area of spheroid surface body boundary free-surface boundary singular surface inside body singular surface above free surface 417 t V V(t)
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From page 418... ...
In the following sections, we describe the problem formulation in section 3 and a more detailed discussion on the desingularized boundary integral method in section 4. Finally we present the results of the computations for the waves caused by a simple disturbance moving below a free surface with forward speed and the results for a fully submerged spheroid moving below a free surface.
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Simi lar to conventional boundary integral methods, it reformu lates the boundary value problem into a boundary integral equation. The difference is that the desingularized method separates the integration and control surfaces, resulting in nonsingular integrals.
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The moving computational window makes it difficult to have a non-uniform grid in the ~ direction with finer spacing near the disturbance. Collocation is used to satisfy the boundary conditions on the surface grid.
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, showing the larger nonlinear effects of the free surface conditions, especially at the troughs. 6.3 Waves generated by a spheroid moving below a free surface In this example, the length scale is chosen to make the length of the spheroid l unity.
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From page 422... ...
For all attempted Froude numbers, the free surface is sucked down and touches the body surface which in turn stops the computation. The linear calculations are not affected by this because the free surface boundary conditions o.o~o -0.002 -o .004 -o .006 \\\/ "-_...
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From page 423... ...
4.0 _ 2.0 _ 0 50 100 150 Ni 200 250 Fig. 9 Sensitivity of body mesh Slender body Haveloclc Doctors and Beck x x x x Farell ~ ~ ~ ~present method (h/L = 0.245)
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. We also performed an energy conservation check for a fixed control volume bounded by the free surface, the body surface, a horizontal bottom and four vertical surfaces representing the truncated far-field boundaries.
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From page 425... ...
17. Schultz, W.W., Cao, Y., and Beck, R.F., "Three-Dimen sional Nonlinear Wave Computation by Desingularized Boundary Integral Method," 5th International Workshop on Water IPaves and Floating Bodies, MaDchester (1990~.
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