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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡丁貴 | |
| dc.contributor.author | Nan-Jing Wu | en |
| dc.contributor.author | 吳南靖 | zh_TW |
| dc.date.accessioned | 2021-06-13T15:21:10Z | - |
| dc.date.available | 2009-07-30 | |
| dc.date.copyright | 2008-07-30 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-22 | |
| dc.identifier.citation | Alves C.J.S., Antunes P.R.S., The method of fundamental solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes, Computers, Materials and Continua, 2005; 2: 251-266.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37198 | - |
| dc.description.abstract | 本論文利用無網格數值方法，建立一個能模擬完全非線性水面波的數值模式。在空間方面，以拉普拉斯方程式(Laplace Equation)基本解(Fundamental Solution) 之線性組合擬合流體速度勢(Velocity Potential)，將前述基本解之中心(Source Point)置於計算邊界以外的位置，僅需由適當少數邊界點上的邊界條件即可進行求解，不需要積分，也不需要處理任何奇異點(Singularity)。在時間方面，利用二階中央差分，將自由液面邊界條件離散成為顯式的差分式，不需要迭代，也不需在時間上做積分，即可推測下個時間步（Time Step）求解所需之自由液面邊界條件。此種離散方式亦稱為跳蛙法（Leap Frog Scheme）。而推算下個時間步自由液面邊界條件需要自由液面梯度，則透過高斯幅狀基底函數(Gaussian Radial Basis Function)來擬合自由液面的水位高程，進而得到求解所需之條件。
本論文先模擬孤立波在三維渠道內之傳遞，並檢查質量與能量之守恒，來證明本數值方法之正確性。然後，再分別模擬二維及三維的問題，來說明本數值方法之適用性。各項數值模擬，均與前人研究之解析解、數值解或實驗結果比較，以說明模擬結果之準確可靠。 | zh_TW |
| dc.description.abstract | A numerical model for fully nonlinear free surface waves is developed in present study, by applying a boundary-type meshless approach with leap frog time marching scheme. Adopting Gaussian Radial Basis Functions to fit the free surface, a non-iterative approach to discretize the nonlinear free surface boundary conditions is formulated. Using the fundamental solutions of the Laplace equation as the solution form of the velocity potential, free-surface wave problems can be solved by collocations at only a few boundary points since the governing equation is automatically satisfied.
The accuracy of present method is verified by comparing the simulated propagation of a solitary wave in a three dimensional flume with an exact solution. The applicability of present model is illustrated by employing it to simulate both two dimensional and three dimensional problems. Good agreement can be found in comparing the results of present numerical model with other schemes, as well as with analytic solutions and available experimental data. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T15:21:10Z (GMT). No. of bitstreams: 1 ntu-97-D90521005-1.pdf: 3045743 bytes, checksum: 24cc1c88631967be68ebef52def95430 (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | Contents
Acknowledgement..........................................Ⅰ Abstract.................................................Ⅱ Abstract (in Hanji) .....................................Ⅲ Contents.................................................Ⅳ Figure Captions..........................................Ⅵ Table List...............................................Ⅹ Ⅰ. Introduction..........................................1 Ⅱ. Mathematical Description..............................7 2.1 Governing Equations...................................7 2.2 Initial Condition and Boundary Conditions.............9 2.2.1 Initial condition...................................9 2.2.2 Boundary conditions at the free surface.............9 2.2.3 Boundary condition on a solid boundary.............10 Ⅲ. Numerical Implementation.............................11 3.1 Radial Basis Functions...............................11 3.2 Time Marching Scheme.................................12 3.3 Collocation for solving the Velocity Potential.......13 3.4 Calculation of the Free Surface Gradient.............14 3.5 Procedures of Numerical Implementation...............16 Ⅳ. Model Verification...................................18 Ⅴ. Applications to 2-D Problems - Wave Propagation in a Wave Flume...............................................22 5.1 Description of the Problem...........................22 5.2 Model Setting........................................24 5.2.1 Arrangement of boundary and source points..........24 5.2.2 Offset distances of source points from the boundary.................................................26 5.2.3 Shape parameters of Gaussian radial basis functions................................................28 5.2.4 Convergence of free surface nodal resolution.......32 5.2.5 Elimination of wave reflection using radiation boundary condition on a gentle slope.....................35 5.3 Numerical Results....................................36 5.3.1 Wave height distributions nearby a piston-type wavemaker................................................36 5.3.2 Second harmonic wave components generated by a high-stroke wavemaker.........................................41 5.3.3 Evolution of monochromatic waves passing over a submerged obstacle.......................................46 Ⅵ. Application to 3-D Problems (Ⅰ) – Run up of a Solitary Wave on a Surface Piercing Vertical Cylinder....55 6.1 Description of the Problem...........................55 6.2 Model setting........................................55 6.3 Numerical Results....................................57 Ⅶ. Application to 3-D Problems (Ⅱ) – Wave Generation by a Submerged Moving Object................................62 7.1 Description of the Problem...........................62 7.2 Model Setting........................................64 7.2.1 Arrangement of boundary and source points..........64 7.2.2 Spacing for free surface nodes.....................67 7.3 Numerical results....................................70 7.3.1 Wave pattern generated by a submerged moving spheroid.................................................70 7.3.2 Drag force exerted on the spheroid.................78 7.3.3 Wave pattern generated by other shaped objects.....83 Ⅷ. Conclusions and Suggestions..........................89 8.1 Conclusions..........................................89 8.2 Suggestions..........................................91 References...............................................93 Figure Captions Fig. 1 The propagation of the solitary wave, for the case of H/h0=0.3..............................................21 Fig. 2 The evolution of the relative mass error, for the propagation of a solitary wave of the case H/h0=0.3......21 Fig. 3 Schematic diagram of boundary and source points arrangement for 2–D problems of wave propagation in a flume....................................................26 Fig. 4 Computed free surface profiles at instant of t=4T for testing the influence of offset distance ratio r_d (in a flume of h=38cm with period and amplitude of wave paddle oscillation 2.75sec and 6.1cm, respectively).............27 Fig. 5 Demonstration of the singularity in case of mal-choosing the shape parameter when fitting the free surface with Gaussian radial basis functions.....................29 Fig. 6 Free surface profiles calculated using present method with various shape parameter ratio, r_d, at the instant of t=T (in the flume of h=38cm with period and amplitude of wave paddle oscillation 2.75sec and 6.1cm, respectively.............................................31 Fig. 7 Free surface gradients generated from the output free surface elevations by using finite difference method, compared with the output results with shape parameter ratio, r_sigma=0.8 and r_sigma=1.0, at the instant of t=T (in a flume of h=38cm with period and amplitude of wave paddle oscillation 2.75sec and 6.1cm, respectively)......32 Fig. 8 Computed free surface profiles at the very moment of t=4T for testing convergence of nodal density (in a flume of h=38cm with period and amplitude of wave paddle oscillation 2.75sec and 6.1cm, respectively).............34 Fig. 9 Free surface profiles at the instant of t=7T in the flume with different flume length (in a flume of h=38cm with period and amplitude of wave paddle oscillation 2.75sec and 6.1cm, respectively).........................36 Fig. 10 Wave evolution nearby the wave paddle for the case of T=0.79sec, S=2.54cm, h=2.00ft.................................................38 Fig. 11 Envelopes of the wave crest and the wave trough nearby the wave paddle for the case of T=0.79sec, S=2.54cm, h=2.00ft.......................................39 Fig. 12 Wave height distributions near the wave paddle of a piston type wavemaker..................................40 Fig. 13 Comparison of predicted deviation from wave maker theory due to finite wave steepness with the experimental data.....................................................40 Fig. 14 Wave evolution nearby the wave paddle for the case of T=2.75sec, S=12.2cm, h=38cm...................................................44 Fig. 15 Time history of free surface elevation at two stations, x = 4.9 m and 8.7 m, for the case of T=2.75sec, S=12.2cm, h=38cm.........................................44 Fig. 16 Comparison between observed, predicted, and numerical surface displacements generated by a sinusoidally-moving wavemaker, for the case of T=2.75sec, S=12.2cm, h=38cm.........................................45 Fig. 17 Numerical results of free surface profile at t=21.8sec along the wave flume, for the case of T=2.75sec, S=12.2cm, h=38cm...................................................46 Fig. 18 Wave flume and locations of wave gages (Ohyama et al., 1994)...............................................48 Fig. 19 Free surface displacements for long monochromatic waves at stations........................................49 Fig. 20 Free surface displacements for short monochromatic waves at stations........................................53 Fig. 21 Arrangement of the collocation points and source points in the vicinity of the cylinder for simulation of the run up of a solitary wave on a surface piercing cylinder.................................................57 Fig. 22 Sequences of a solitary wave running up on a vertical cylinder in a three-dimensional view, for the case of H/h0=0.3.........................................58 Fig. 23 Sketch of a spheroid and variables associated with its motion...............................................65 Fig. 24 Schematic diagram of the arrangement of boundary and source points for the problem of wave generation by a submerged moving object..................................66 Fig. 25 Computed free surface profiles of y=0 at stage of xc=2L for testing convergence of free surface nodal density (the spheroid in diameter-to-length ratio 0.1 with the diameter-to-submergence ratio 1.0 and Froude number 0.5).....................................................68 Fig. 26 Comparison of free surface contours calculated in constant nodal spacing with those contours calculated in variant nodal spacing at stage of xc=4L (the spheroid in diameter-to-length ratio 0.1 with the diameter-to-submergence ratio 1.0 and Froude number 0.5).............70 Fig. 27 Evolution of free surface elevation contours for the case of a spheroid in diameter-to-length ratio 0.1 with the diameter-to-submergence ratio 1.0 and Froude number 0.5...............................................72 Fig. 28 Evolution of the central free surface profile for the case of a spheroid in diameter-to-length ratio 0.1 with the diameter-to-submergence ratio 1.0 and Froude number 0.5...............................................76 Fig. 29 Wave pattern in a three-dimensional view at stage of xc=8L for the case of a spheroid in diameter-to-length ratio 0.1 with the diameter-to-submergence ratio 1.0 and Froude number 0.5........................................76 Fig. 30 Computed central free surface profile at steady state compared with other numerical results, for the case of a spheroid in diameter-to-length ratio 0.1 with the diameter-to-submergence ratio 1.0 and Froude number 0.5......................................................78 Fig. 31 Wave patterns in a three-dimensional view at stage of xc=8L for the case of a spheroid in diameter-to-length ratio 0.245 with diameter-to-submergence ratio 0.816.....79 Fig. 32 Comparison of resistance coefficient computed by present model with other numerical results, for the case of a spheroid in diameter-to-length ratio 0.245 with diameter-to-submergence ratio 0.816......................83 Fig. 33 Bodies considered in wave resistance problem in the work of Lalli (1997).................................84 Fig. 34 Wave patterns in a three-dimensional view at stage of xc=8L for both bodies for cases of diameter-to-length ratio 0.2, diameter-to-submergence ratio 1.0 and Froude number 0.447 and 0.448, respectively.....................86 Fig. 35 Comparison of present results with experimental data and the numerical results of Lalli (1997) for the case of the spheroid in diameter-to-length 0.2, diameter to submergence ratio 1.0, and Froude number 0.447........87 Fig. 36 Comparison of present results with experimental data and the numerical results of Lalli (1997) for the case of streamlined cylinder in diameter-to-length 0.2, diameter-to-submergence ratio 1.0, and Froude number 0.448....................................................88 Table List Table 1 List of Ursell et al.'s (1960) finite amplitude wave generation conditions...............................37 | |
| dc.language.iso | en | |
| dc.title | 以高斯幅狀基底函數之無網格方法數值模擬完全非線性水面波 | zh_TW |
| dc.title | Numerical simulation of fully nonlinear surface waves by meshless method with Gaussian radial basis functions | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 蘇青和,林銘崇,陳正宗,許榮中,楊德良,許泰文,蔡武廷 | |
| dc.subject.keyword | 無網格數值方法,非線性水波,基本解,高斯輻狀基底函數, | zh_TW |
| dc.subject.keyword | Meshless Numerical Method,Nonlinear Water Wave,Gaussian Radial Basis Function,Fundamental Solution, | en |
| dc.relation.page | 103 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-07-23 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| 顯示於系所單位： | 土木工程學系 | |
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