The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Stability and Accuracy of a Non-Linear Model for the Wave Resistance Problem
Stability and Accuracy of a Non-Linear Model for the Wave Resistance Problem
Pages 629-642
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From page 629... ...
In addition, the free surface is not known a priori because it is part of the solution. Consequently panels must be associated either with the calm free-surface (with the actual free-surface represented by means of a Maclaurin expansion of the prevailing boundary conditions)
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From page 630... ...
If a Rankine source rather than a Havelock source is used then perhaps an even greater problem presents itself: how large an expanse of the free surface in the vicinity of the hull needs to be modelled using additional panels and how should the resolution of this region be chosen? The manner in which the source density is distributed algebraically on each panel will also affect the solution.
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From page 631... ...
represents the outward normal vector on the hull surface, 1 represents a distance measured along a double-body streamline measured positive in the locally upstream direction, Up is the ship speed, g is the acceleration due to gravity and ~ represents the wave elevation. The last two boundary conditions are non-linear and result from Maclaurin expansions of the exact boundary conditions prevailing on the free surface [1]
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From page 632... ...
In addition, an optional facility exists to position extra hull panels between water-line stations defined by the free-surface nodes so that the hull panel density (defined as the number of stream-wise hull panels per free-surface panel) can assume any integer value.
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From page 633... ...
Absence of a data point in any of the accompanying graphs indicates that the algorithm failed to converge within the specified tolerance (often but not always this meant that the algorithm diverged; occasionally the root mean square of the residuals meandered about a mean value above the selected tolerance - such runs were deemed to have failed even though the associated wave resistance had apparently converged to within ~ finer tolerance)
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From page 634... ...
The stability of panel methods for the linear problem has been analysed recently using Fourier techniques by Sclavounos and Nakos [133. They found that the numerical damping associated with upwind finite difference schemes decreases as the grid becomes finer or as the number of upstream nodes included in the scheme at a particular control point increases.
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From page 635... ...
The first type, labelled mode 1, single-patch, uses panel geometries on the calm free surface which are independent of Froude number but which are kept constant with respect to the ship-length. The hull panels are organised so that the same number of panels is used at each station.
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From page 636... ...
Ni, S Y "Higher Order Panel Methods for Potential Flows with Linear or Non-Linear Free Surface Boundary Conditions", Chalmers University of Technology, 1987.
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From page 637... ...
"Numerical Prediction of Steady Ship Waves of Series 60 Model and Comparison with Experimental Measurements", Proceedings of the 18th International Towing Tank Conference, Kobe, October 1987. 3 · ~ · ~ · · ~ · · · ·/ 13.S '2 ~ ~ 6 ' ' 3'.o ' ' ' '3'.4 ~i g 2 Con Use and expe r i mend A 637 3.S Hi me F i me G r i As
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From page 638... ...
. / V Fr F1g ~ Effect of Grid Resolution 638 ~ , X10 -1 8
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From page 639... ...
1.8 /! xt Fig 6 Effect of Hull Panel Density 639 3.8
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From page 640... ...
.~.,.~ ,8~ . 2.9 5.0 3.4 3.8 X10-t F r F8g 7 Effect of Free-Surface Panel Elevat8on 1000~8C ~ Taylor W X spine -Experiment Mode 2, Multi-Patch 15% Panel Elevat80n eX/ ~_r / , ~ , ~ ~ 3.0 8r F"8g 8 Effect of Advect-8on Scheme 640 X10 18
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From page 641... ...
MOW ~ Spilne Advection Scheme 4.00 0 Taylor Adveictlon Scheme 3.SO 3r 00 2eSO 2.00 \.50 \.00 O.S~ D.00.\,80 Mode 2, Multi-Patch Zero Panel Elevation /d / ~ / / 2 I ~ ~ ~ r 2~;0 3~{JO F r Fig 9 Saline Calculation for Zero Panel Elevation t000 ~ C ~ Splir~le Schel~le In ~ ~ Taylo'~ Scl-lerrie In = 4 3 2 ~ to 3.40 3.8U X10 -1 = Mode 2, Multi-Pa-Uch 15~o Panel Elev~t~ion NO insufficient computer memory to lowest Denude number- when n = 1 2r my/ 3.0 3,4 F." -fig -10 E-F-Fec-t of Spl-ilne Michelle For In = 12 641 X10 -1 3.e
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From page 642... ...
· Present Method -- Experiment Mode 2, Multi-Patch 15= Panel Elevation Taylor Advection Scheme o ~ a/ ,~ Q /` a _ 1.8 2.2 2.6 3.0 F r F1g 11 Comparison with Other Non-LinQar methods Copyright (C) Controller HMSO London 1989 3.4 3.8 X10-1 642
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