Sloshing Simulation of Standing Wave With a Time-Independent Finite Difference Method for Euler Equations
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摘要: 研究在二维水槽带非线性自由面边界条件的Euler方程的数值解,数值模拟了驻波的波高.将不规则的物理区域变换为一个固定的正方形计算区域,在计算区域使用交错网格技术的目的是准确捕捉流场瞬间的波高值,应用由Bang-fuh Chen建立的时间无关有限差分方法求解不可压缩无粘Euler方程的数值解.通过数值结果表明,数值解很好地吻合分析解和以前出版的文献结果.从数值解可以看出,非线性现象和拍的现象非常明显,同时数值模拟了带初始驻波的水平激励和垂直激励运动,具有很好的数值效果.
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关键词:
- Euler方程 /
- 有限差分方法 /
- 数值模拟 /
- Crank-Nicolson格式
Abstract: The numerical solutions of standing wave for Euler equations with nonlinear free surface boundary condition in a two dimensional tank were solved.The irregular tank was mapped onto a fixed square domain through proper mapping functions and a staggered mesh system was employed in a two dimensional tank in order to calculate the elevation of the transient fluid.A time-independent finite difference method, which was developed by Bang-fuh Chen,was applied and was used to solve Euler equations for incompressible and inviscid fluid.The numerical solutions agree well with analytic solutions and previously published results.The nonlinear and beating phenomena are very clear and the sloshing of surge and heave motions with initial standing wave are presented.-
Key words:
- Euler equations /
- finite difference method /
- numerical simulation /
- Crank-Nicolson scheme
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[1] Abramson H N. The dynamic behavior of liquids in moving containers[R]. SP-106, Washington D C: National Aeronautics and Space Administration, 1966. [2] Miles J W. Nonlinear surface waves in closed basins[J]. Journal of Fluid Mechanics, 1976, 75(3): 419-448. doi: 10.1017/S002211207600030X [3] Miles J W. Internally resonant surface waves in a circular cylinder[J]. Journal of Fluid Mechanics, 1984, 149(12): 1-14. doi: 10.1017/S0022112084002500 [4] Miles J W. Resonantly forced surface waves in a circular cylinder[J]. Journal of Fluid Mechanics, 1984, 149(12): 15-31. doi: 10.1017/S0022112084002512 [5] Hutton R E. An investigation of resonant nonlinear nonplannar free surface oscillations of a fluid[R]. Washington D C: National Aeronautics and Space Administration, 1963. [6] Faltisen O M. A nonlinear theory of sloshing in rectangular tanks[J]. Journal of Ship Research, 1974, 18(4): 224-241. [7] Waterhouse D D. Resonant sloshing near a critical depth[J]. Journal of Fluid Mechanics, 1994, 281(12): 313-318. doi: 10.1017/S0022112094003125 [8] Faltisen O M. Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth[J]. Journal of Fluid Mechanics, 2000, 407(3): 201-234. doi: 10.1017/S0022112099007569 [9] Whitham G B. Nonlinear dispersion of water waves[J]. Journal of Fluid Mechanics, 1967, 27: 399-412. doi: 10.1017/S0022112067000424 [10] Balk A M. A Lagrangian for water waves[J]. Physics of Fluids, 1996, 8(2): 416-420. doi: 10.1063/1.868795 [11] La Rocca M, Mele P, Armenio V. Variational approach to the problem of sloshing in a moving container[J]. Journal of Theoretical and Applied Fluid Mechanics, 1997, 1(4): 280-310. [12] Sirovich L. New Perspectives in Turbulence[M]. Berlin: Springer, 1991. [13] Sriram V, Sannasiraj S A, Sundar V. Numerical simulation of 2D sloshing waves due to horizontal and vertical random excitation[J]. Applied Ocean Research, 2006, 28(1): 19-32. doi: 10.1016/j.apor.2006.01.002 [14] Frandsen J B. Numerical bridge deck studies using finite elements. part Ⅰ: flutter[J]. Journal of Fluids and Structures, 2004, 19(2): 171-191. doi: 10.1016/j.jfluidstructs.2003.12.005 [15] Lin P Z. A gixed-grid model for simulation of a moving body in free surface flows[J]. Computers & Fluids, 2007, 36(3): 549-561. [16] Lhner R, Yang C, On··ate E. On the simulation of flows with violent free surface motion[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(41/43): 5597-5620. doi: 10.1016/j.cma.2005.11.010 [17] Chen Y H, Hwang W S, Hao C. Numerical simulation of the three-dimensional sloshing problem by boundary element method[J]. Journal of the Chinese Institute of Engineers, 2000, 23(3): 321-330. doi: 10.1080/02533839.2000.9670552 [18] Chen B F. Nonlinear hydrodynamic pressures by earthquakes on dam face with arbitrary reservoir shapes[J]. Journal of Hydraulic Research, 1994, 32(30): 401-413. doi: 10.1080/00221689409498742 [19] Chen B F, Nokes R. Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular tank[J]. Journal of Computational Physics, 2005, 209(1): 47-81. doi: 10.1016/j.jcp.2005.03.006 [20] Chen B F. Viscous fluid in a tank under coupled surge, heave and pitch motions[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2005, 131(5): 239-256. doi: 10.1061/(ASCE)0733-950X(2005)131:5(239) [21] Wu C H, Chen B F. Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method[J]. Ocean Engineering, 2009, 36(6): 500-510. doi: 10.1016/j.oceaneng.2009.01.020 [22] Lapidus L, Pinder G F. Numerical Solution of Partial Differential Equations in Science and Engineering[M]. New York: John Wiley and Sons, 1982. [23] Hoffman J D. Numerical Methods for Engineers and Scientists[M]. New York: McGraw-Hill Inc, 1993. [24] Nakayama T, Washizu K. The boundary element method applied to the analysis of two dimensional nonlinear sloshing problems[J]. International Journal for Numerical Methods in Engineering, 1981, 17(11): 1631-1646. doi: 10.1002/nme.1620171105 [25] Wu G X. Second order resonance of sloshing in a tank[J]. Ocean Engineering, 2007, 34(17/18): 2345-2349. doi: 10.1016/j.oceaneng.2007.05.004
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