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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
dc.contributor.author | Yu-Ting Hong | en |
dc.contributor.author | 洪毓廷 | zh_TW |
dc.date.accessioned | 2021-06-16T22:58:18Z | - |
dc.date.available | 2021-02-22 | |
dc.date.copyright | 2021-02-22 | |
dc.date.issued | 2021 | |
dc.date.submitted | 2021-02-03 | |
dc.identifier.citation | [1] J. A. Trangenstein and P. Colella, “A higher-order godunov method for modeling finite deformation in elastic-plastic solids,” Communications on Pure and Applied mathematics, vol. 44, no. 1, pp. 41–100, 1991. 1, 16 [2] G. Miller and P. Colella, “A high-order eulerian godunov method for elastic–plastic flow in solids,” Journal of computational physics, vol. 167, no. 1, pp. 131–176, 2001. 1, 11, 13, 16, 19, 28, 30, 31, 33 [3] D. J. Hill, D. Pullin, M. Ortiz, and D. Meiron, “An eulerian hybrid weno centered-difference solver for elastic–plastic solids,” Journal of Computational Physics, vol. 229, no. 24, pp. 9053–9072, 2010. 1 [4] C.-W. Shu, “Essentially non-oscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws,” in Advanced numerical approximation of nonlinear hyperbolic equations. Springer, 1998, pp. 325–432. 19, 20 [5] R. J. LeVeque et al., Finite volume methods for hyperbolic problems. Cambridge university press, 2002, vol. 31. 19 [6] S. Ndanou, N. Favrie, and S. Gavrilyuk, “Criterion of hyperbolicity in hyperelasticity in the case of the stored energy in separable form,” Journal of Elasticity, vol. 115, no. 1, pp. 1–25, 2014. 12, 16, 49 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/64738 | - |
dc.description.abstract | 在本論文中,我們使用五階WENO 方法搭配二階Runge-Kutta 方法,來數值求解尤拉座標中的等向性超彈性(isotropic hyper-elastic)模型。我們在尤拉座標系中將超彈性材料方程式公式化為雙曲守恆系統;然而除了方程式以外,仍有額外的兩個條件需要被滿足,這和氣體動力學的情況並不相同,一個條件是反變形梯度(inverse deformation gradient)的相容性條件,另一個則是密度的一致性條件。當使用WENO 方法求解該系統時,相容性條件會作為擴散項加入反變形梯度的演化方程式,而一致性條件亦作為鬆弛項加入該條方程式,我們透過數值模擬來驗證方法的可行性。 本研究包含了四項數值模擬實驗,第一項實驗顯示:我們的方法對於平滑解達到了二階收斂性;後三項實驗則是對於黎曼問題的測試,這些結果展現了WENO方法對於求解不連續性解的準確性。 | zh_TW |
dc.description.abstract | In this thesis, we apply a fifth-order weighted essentially non-oscillatory(WENO-5) scheme together with a second-order Runge-Kutta method to solve isotropic hyper-elastic models in Eulerian coordinate numerically. We formulate equations of hyper-elastic materials in Eulerian frame of reference as a system of hyperbolic conservation laws. However, additional constraints should be satisfied, which are different from the gas dynamics. One is a compatibility condition for inverse deformation gradient. The other is a consistency condition for density. In applying WENO method to solve this system, the compatibility condition is added as a pseudo-diffusion term in the evolution equation of the inverse deformation gradient, whereas the consistency condition is also added in this evolution equation as a relaxation term. The feasibility is shown by numerical tests. Four numerical simulations are included in this thesis. The first case demonstrates that our method attains second-order convergence for smooth solutions. And the last three cases, which are the tests for Riemann problems, show the accuracy of our method for solving solutions with discontinuities. | en |
dc.description.provenance | Made available in DSpace on 2021-06-16T22:58:18Z (GMT). No. of bitstreams: 1 U0001-0202202116422000.pdf: 4559506 bytes, checksum: 790ac51710b9367e61128d2872cd090e (MD5) Previous issue date: 2021 | en |
dc.description.tableofcontents | Contents Abstract i 1 Introduction 1 2 Equation Formulations 3 2.1 Conservation of mass . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Conservation of momentum . . . . . . . . . . . . . . . . . . . 5 2.3 Conservation of energy . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Constitutive law . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Compatibility condition for deformation gradients . . . . . . . 12 2.6 Inverse deformation gradient and its compatibility condition . 13 2.7 Governing equations . . . . . . . . . . . . . . . . . . . . . . . 16 3 Numerical Method 19 3.1 Weighted essentially non-oscillatory(WENO) scheme . . . . . 19 3.2 Pseudo-diffusion terms for the compatibility condition . . . . . 27 3.3 Relaxation terms for the consistency condition . . . . . . . . . 30 4 Numerical Simulations 33 4.1 Convergence test for smooth cases . . . . . . . . . . . . . . . . 33 4.2 Riemann problem: Sod shock tube test . . . . . . . . . . . . . 38 4.3 Riemann problem: the Mooney-Rivlin model . . . . . . . . . . 44 4.4 Riemann problem: the stored energy in a separable form . . . 49 5 Conclusions 57 Reference 59 | |
dc.language.iso | en | |
dc.title | 使用WENO方法來研究在尤拉座標下彈性流體之數值模擬 | zh_TW |
dc.title | Numerical Simulations of Elastic Flows in Eulerian Coordinate Using WENO Scheme | en |
dc.type | Thesis | |
dc.date.schoolyear | 109-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 薛克民(Keh-Ming Shyue),舒宇宸(Yu-Chen Shu) | |
dc.subject.keyword | 權重無震盪法,彈性,相容性條件, | zh_TW |
dc.subject.keyword | WENO,elasticity,compatibility condition, | en |
dc.relation.page | 59 | |
dc.identifier.doi | 10.6342/NTU202100401 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2021-02-04 | |
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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