The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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A Boundary Integral Formulation for Free Surface Viscous and Inviscid Flows about Submerged Bodies
A Boundary Integral Formulation for Free Surface Viscous and Inviscid Flows about Submerged Bodies
Pages 469-480
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From page 469... ...
Piva University di Roma "La Sapienza" Roma, Italy Abstract The possibility to generate numerical models based on a boundary integral formulation for rotational free surface flows, either viscous or inviscid, is explored with the purpose to maintain some of the computational efficiency proper of potential flow approaches. A simple method for the simulation of the unsteady nonlinear behavior of the free surface has been derived, starting from a mathematical model which decouples the kinematical and the dynamical aspects of the flow field, without introducing the potential approximation.
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From page 470... ...
It is on these theoretical topics that the integral formulation for viscous flow has found their best application, due to the simple analysis of the proper boundary conditions. More recently, due to the developments of the boundary element methods, integral formulations have received new interest for the numerical simulation of viscous Bows.
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From page 471... ...
is the Bernoulli group. For the sake of clarity it is to be remarked the difference between the traction vector tj involved in the boundary conditions and the modified traction vector tj (tj = tj + 2u2 + II)
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Consequently one of the boundary conditions for viscous flow should be relaxed, due to the lowering of the order of the partial differential equation. For this limiting case a boundary integral formulation is directly derived from the one valid for Navier Stokes equations, rather than from the differential model.
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From page 473... ...
models In both the integral formulations presented in the previous sections the kinematical and dynamical parts of the flow problem are strictly coupled. The proper boundary conditions for the free surface problem in the coupled models is introduced here in some details in order to show the differences with the corresponding treatment in decoupled models (splitting of kinematics and dynamics)
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From page 474... ...
In this case the definition of the boundary conditions is not as direct as for the coupled models. A general kinematical representation and the dynamical boundary condition In this section a purely kinematical integral representation will be recovered as a semplified version of the integral formulation for inviscid flows.
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From page 475... ...
This nonlinear evolution equation for the tangential velocity component gives the free boundary condition for the two boundary integral equation (25)
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From page 476... ...
The strict relationship with the coupled models based on the integral formulation for viscous and inviscid flows, have been discussed. While the numerical solution of the Fredholm integral equation gives very satisfactory results, the numerical tecnique for an efficient as well as accurate resolution of the Cauchy type equation is to be completed.
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From page 477... ...
[8] Nedelec, J.C., (1977~: " Integral Equations with Non Integrable Kernels, Integral Equations and Operator Theory, Vol.
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From page 478... ...
3. Free surface configuration vs time Fr = .95 D = 1 Submergence h = 3 Dt = .25 t= 75 0 t = 80 a o t = 85 o t = 90 478
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From page 479... ...
7. Pressure distribution on the cylinder.
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