无结构网格二维河口海岸水动力数值模式的建立及其应用
An unstructured mesh two-dimensional coastal and estuarine hydrodynamic numerical model and its application
-
摘要: 为完全拟合河口近海复杂岸线和工程结构以及有效局部加密,设计并建立了一个无结构三角形网格二维河口海岸水动力数值模式。空间离散主要基于有限体积法以保证守恒性,时间积分采用预估修正法以提高精度。水位在三角形网格中心通过连续方程求解;水平x方向和y方向的流速U和V均在网格边中点上通过动量方程求解。流速平流项的求解中采用了TVD格式。TVD流速平流通量为一个一阶迎风格式通量和一个二阶格式通量的组合,一阶格式通量和二阶格式通量根据流速的局部分布情况得出配比,最终组合得到TVD通量。TVD格式具有低耗散和无频散的优点,提高了模式的稳定性。应用实测资料验证建立的模式,结果显示水位、流速和流向的计算值与实测值均符合良好。Abstract: In order to perfectly fit complex coastlines and project structures in coastal and estuarine areas, an unstructured mesh two-dimensional coastal and estuarine hydrodynamic numerical model is established. Finite-volume method is used in spatial discretization to guarantee conservation and predictor-corrector method is used in temporal to improve accuracy. Elevation is solved at the centre of the triangular cell by continuity equation, while horizontal x-direction and y-direction velocities are solved at the middle of grid sides by momentum equations.In calculating velocity advection, TVD scheme is adopted. TVD flux of velocity advection is a combination of the first-order upwind flux and a second-order scheme flux.The proportion of each flux contributing to TVD flux is decided by the local velocity distribution. TVD scheme is low-diffusive and non-dispersive, which improves the stability of the model. Observed data are used to validate the model. Results show that elevation, flow velocity and flow direction are all well matched between calculated values and observed ones.
-
Key words:
- unstructured mesh /
- hydrodynamic numerical model /
- TVD scheme
-
朱建荣.海洋数值计算方法和数值模式[M].北京:海洋出版社,2003. BLUMBERG A F, MELLOR G. A Description of a Three-Dimensional Coastal Ocean Circulation Model[M]. Washington, DC: American Geophysical Union,1987. LYNCH D R, NAIMIE C E. The M2 tide and its residual on the outer banks of the Gulf of Maine[J]. J Phys Oceanogr, 1993, 23: 2222—2253. NAIMIE C E. Georges Bank residual circulation during weak and strong stratification periods: Prognostic numerical model results[J]. J Geophys Res, 1996, 101(C3): 6469—6486. PAIN C C, PIGGOTT M D, GODDARD A J H, et al. Three-dimensional unstructured mesh ocean modeling[J]. Ocean Modelling, 2005, 10: 5—33. CHEN C, LIU H, BEARDSLEY R C. An unstructured grid, finite-volume, three-dimensional, primitive equation ocean model: Application to coastal ocean and estuaries[J]. Journal of Atmospheric and Oceanic Technology, 2003, 20:159—186. CASSULI V, ZANOLLI P. Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems[J]. Mathematical and Computer Modelling, 2002, 36: 1131—1149. CASSULI V, ZANOLLI P. High resolution methods for multidimensional Advection-diffusion Problems in free-surface hydrodynamics [J]. Ocean Modelling, 2005, 10: 137—151. HAM D A, PIETRZAK J, STELLING G S. A scalable unstructured grid 3-dimensional finite volume model for the shallow water equations [J]. Ocean Modelling, 2004, 10: 153—169. HAM D A, KRAMER S C, STELLING G S, et al. The symmetry and stability of unstructured mesh C-grid shallow water models under the influence of Coriolis [J]. Ocean Modelling, 2007, 16: 47—60. ZHANG Y, BAPTISTA A M, MYERS E P. A cross-scale model for 3D baroclinic circulation in estuary-plume-shelf systems: Ⅰ. Formulation and skill assessment [J]. Continental Shelf Research, 2004, 24: 2187—2214. 赵棣华,戚晨,庾维德,等.平面二维水流-水质有限体积法及黎曼近似解模型[J]. 水科学进展,2000,11(4):368—374. 李未,张长宽,王如云.基于无结构网格有限体积法的风暴潮数值预报模式[J]. 热带海洋学报,2007,26(2):9—14. JAMES I D. Advection schemes for shelf sea models [J]. Journal of Marine Systems, 1996, 8: 237—254. SWEBY P K. High resolution schemes using flux limiters for hyperbolic conservation laws[J]. SIAM J Numer Anal,1984, 21: 995—1011 ROE P L. Characteristic-based scheme for the Euler equations[J]. Ann Rev Fluid Mech, 1986, 18:337-365 YANG H Q, PRZEKWAS A J. A comparative study of advanced shock capturing schemes applied to Burgers' equation[J]. J Comp Phys, 1992, 102:139-159. REID R Q, BODINE B R. Numerical model for storm surges in Galveston Bay[J]. Journal of the Waterways and Harbors,1968, 94 (WW1): 33—57. HIBBERD S, PEREGRINE D H. Surf and run-up on a beach: a uniform bore[J]. Journal of Fluid Mechanics, 1979, 95(2):323—345. LIN B, FALCONER R A. Three-dimensional layer-integrated modeling of estuarine flows with flooding and drying[J]. Estuarine, Coastal and Shelf Science, 1997, 44:737-751. OEY L Y. A wetting and drying scheme for POM[J]. Ocean Modelling, 2005, 9:133-150.
点击查看大图
计量
- 文章访问数: 1700
- HTML全文浏览量: 11
- PDF下载量: 1827
- 被引次数: 0