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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 薛克民(Keh-Ming Shyue) | |
| dc.contributor.author | Yen-Chung Hung | en |
| dc.contributor.author | 洪彥仲 | zh_TW |
| dc.date.accessioned | 2022-11-24T03:44:26Z | - |
| dc.date.available | 2021-07-23 | |
| dc.date.available | 2022-11-24T03:44:26Z | - |
| dc.date.copyright | 2021-07-23 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-07-19 | |
| dc.identifier.citation | 1. D. Bale, R. J. LeVeque, S. Mitran, and J. Rossmanith. A wave-propagation method for conservation laws or balance laws with spatially varying flux functions. SIAM J Sci. Comp., 24, pages 266-278, 2002 2. R. Barros, S. L. Gavrilyuk, and V. M. Teshukov. Dispersive nonlinear waves in two-layer flows with free surface. i. model derivation and general properties. 2007 3. C. Bassi, L. Bonaventura, S. Busto, and M. Dumbser. A hyperbolic reformulation of the serre-green-naghdi model for general bottom topographies. arXiv:2003.14309v1 [math.NA], 2020 4. A. Bayliss, M. Gunzburger, and E. Turkel. Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM J. Appl. Math., 42(2), pages 430–451, 1982 5. T. B. Benjamin, J. L. Bona, and J. J. Mahony. Model equations for long waves in nonlinear dispersive systems. Series A, Mathematical and Physical Sciences, 272 (1220), pages 47–78, 1972 6. M. J. Castro and A. M. Ferreiro Et. Al. 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A modified galerkin/finite element method for the numerical solution of the serre-green-naghdi system. Int. J. Numer. Meth. Fluids 2017; 83, pages 755–778, 2016 26. O. Le Metayer, S. Gavrilyuk, and S. Hank. A numerical scheme for the green–naghdi model. Journal of Computational Physics 229, pages 2034–2045,2009 27. S. Noelle, N. Pankratz, G. Puppo, and J. R. Natvig. Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. Journal of Computational Physics 213, page 474–499, 2005 28. P. J. Olver. Euler operators and conservation laws of the bbm equation. Math. Proc. Camb. Phil. Soc., 85, pages 143–160, 1979 29. J. P. A. Pitt, C. Zoppou, and S. G. Roberts. Behaviour of the serre equations in the presence of steep gradients revisited. arXiv:1706.08637v1 [math NA], 2017 30. A. Samii and C. Dawson. An explicit hybridized discontinuous galerkin method for serre–green–naghdi wave model. Comput. Methods Appl. Mech. Engrg. 330, pages 447–470, 2017 31. F. J. Seabra-Santos, D. P. Renouard, and A. M. Temperville. Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J. Fluid Mech., vol.176, pages 117–134, 1985 32. F. Serre. Contribution to the study of permanent and non-permanent flows in channels. La Houille Blanche, (6), page 830–872, 1953 33. B. van Leer. Towards the ultimate conservative difference schemes. v: a second-order sequel to godunov’s method. J. Comput. Phys. 32(1), pages 101–136,197 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/81344 | - |
| dc.description.abstract | 在這篇論文中，我們對於非靜水色散模型如BBM模型及SGN模型做了解析及數值的研究。我們推導了週期性行波解及Whitham方程作為數值方法的驗證。此外，我們在數值結果上比較了原始模型及他們各自的雙曲線模型。兩個雙曲線模型都與原始模型在數值結果上相當吻合。而後，我們討論了在計算包含水底地形的SGN模型時，數值方法的處理。我們模仿了[17]、[1]和[27]中描述的方法，並提出了一種保持靜止狀態和穩態解的數值方法。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-24T03:44:26Z (GMT). No. of bitstreams: 1 U0001-1607202116315700.pdf: 11313498 bytes, checksum: c93bc57dee6fed09c3bca9c0ba72fdd5 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xvii 1 Introduction 1 1.1 Motivation 1 1.2 Derivation of SGN equation with topography 2 2 Benjamin-Bona-Mahony model 9 2.1 Periodic wave solution 10 2.2 Dispersion relation 14 2.3 Numerical method 17 2.4 Hyperbolic variance 18 2.4.1 Periodic wave solution 21 2.4.2 Dispersion relation 25 2.4.3 Numerical method 29 2.5 Numerical results 32 2.5.1 Periodic traveling wave 32 2.5.2 Dispersive shock wave 35 3 Serre-Green-Naghdi model without topography 39 3.1 Periodic wave solution 39 3.2 Dispersion relation 44 3.3 Numerical method 46 3.4 Hyperbolic variance for SGN equation 49 3.4.1 Solitary wave solution 51 3.4.2 Dispersion relation 52 3.4.3 Numerical method 54 3.5 Numerical results 57 3.5.1 Solitary wave 57 3.5.2 Dispersive shock wave 58 4 Serre-Green-Naghdi model with topography 63 4.1 Saint-Venant equation 64 4.1.1 Numerical method 65 4.1.2 Numerical results 68 4.2 SGN equation 71 4.2.1 Steady state solution 71 4.2.2 Numerical method 73 4.2.3 Numerical results 77 5 Conclusion 79 References 81 Appendix A-Numerical method 85 A.1 Numerical algorithm of solving hyperbolic system 85 A.2 Elliptic part of BBM equation 88 A.3 Elliptic part of SGN equation 89 Appendix B-Analytic derivation 91 B.1 Whitham system and bounds for DSW of BBM equation 91 B.2 Coordinate transformation between Eulerian and Lagrangian 95 B.3 Whitham system and bounds for DSW of SGN equation 97 B.4 Steady state solution for Saint-Venant equation 101 B.5 Hyperbolic-Elliptic formulation of SGN equation with topography 103 | |
| dc.language.iso | en | |
| dc.subject | 地形學 | zh_TW |
| dc.subject | 乾燥態 | zh_TW |
| dc.subject | Saint-Venant方程 | zh_TW |
| dc.subject | 平衡態結構 | zh_TW |
| dc.subject | 色散震波 | zh_TW |
| dc.subject | Serre-Green-Naghdi方程 | zh_TW |
| dc.subject | Benjamin-Bona-Mahony方程 | zh_TW |
| dc.subject | dispersive shock wave | en |
| dc.subject | Saint-Venant equation | en |
| dc.subject | dry state | en |
| dc.subject | topography | en |
| dc.subject | Benjamin-Bona-Mahony equation | en |
| dc.subject | Serre-Green-Naghdi equation | en |
| dc.subject | well-balanced scheme | en |
| dc.title | 非靜水淺水流的雙曲線模型的數值研究 | zh_TW |
| dc.title | A numerical study of hyperbolic models for non-hydrostatic shallow water flow | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳宜良(Hsin-Tsai Liu),郭志禹(Chih-Yang Tseng) | |
| dc.subject.keyword | Benjamin-Bona-Mahony方程,Serre-Green-Naghdi方程,色散震波,平衡態結構,地形學,乾燥態,Saint-Venant方程, | zh_TW |
| dc.subject.keyword | Benjamin-Bona-Mahony equation,Serre-Green-Naghdi equation,dispersive shock wave,well-balanced scheme,topography,dry state,Saint-Venant equation, | en |
| dc.relation.page | 105 | |
| dc.identifier.doi | 10.6342/NTU202101519 | |
| dc.rights.note | 同意授權(限校園內公開) | |
| dc.date.accepted | 2021-07-19 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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