[1].参考文献 [2]KIRBY J T, WEI G, CHEN Q, et al.FUNWAVE 1.0. Fully nonlinear Boussinesq wave model. Documentation and user' s manual[J]. University of Delaware, 1998. [3]SHI F Y, KIRBY J T, HARRIS J C, et al.A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation[J], Ocean Modelling, 2012, 43-44(2):36-51. [4]WEI G, KIRBY J T, GRILLI S T, et al.A fully nonlinear Boussinesq model for surface wavesI. Highly nonlinear,unsteady waves[J].Journal of Fluid Mechanics, 1995, 294(-1):71-92 [5]MADSEN P A, S?RENSEN O R.A new form of the Boussinesq equations with improved linear dispersion characteristicsPart 2: A slowly-varying bathymetry[J].Coast Engrg, 1992, 18(3-4):183-204 [6]LYNETT P, LIU L F.A two-layer approach to wave modeling[J].Proc R Soc Lond A, 2004, 460(2049):2637-2669 [7]孙家文，朱桐，房克照，等.基于加速的类波浪传播变形数值模型[J].海洋工程, 2020, 38(02):111-119 [8]SUN J W, ZHU T, FANG K Z, et al.A GPU accelerated Boussinesq wave propagation model[J].The Ocean Engineering, 2020, 38(02):111-119 [9]YUAN Y, SHI F Y, KIRBY J T, et al.FUNWAVE‐GPU: Multiple‐GPU Acceleration of a Boussinesq-Type Wave Model[J].Journal of Advances in Modeling Earth Systems, 2020, 12(5):1-19 [10]孙家文，房克照，刘忠波，等.关于型水波方程理论和应用研究的综述[J].海洋学报, 2020, 42(5):1-11 [11]SUN J W, FANG K Z, LIU Z B, et al.A review on the theory and application of Boussinesq-type equations for water waves[J].Haiyang Xuebao, 2020, 42(5):1-11 [12]LIU Z B, FANG K Z, CHENG Y Z.A new multi-layer irrotational Boussinesq-type model for highly nonlinear and dispersive surface waves over a mildly sloping seabed[J]. Journal of Fluid Mechanics, 2018, 842:323-353. [13]MADSEN P A, FUHRMAN D R.High-order Boussinesq-type modeling of nonlinear wave phenomena in deep and shallow water. In Advances in Numerical Simulation of Nonlinear Water Waves [M]. (ed. Q. W. Ma). World Scientific Publishing, 2010. [14]OHYAMA T, KIOKA W, TADA A.Applicability of numerical models to nonlinear dispersive waves[J].Coastal Engineering, 1995, 24(3-4):297-313 [15]NWOGU O.Alternative Form of Boussinesq Equations for Nearshore Wave Propagation[J].Journal of Waterway Port Coastal & Ocean Engineering, 1993, 119(6):618-638 [16]GOBBI M F, KIRBY J T.Wave evolution over submerged sills: tests of a high-order Boussinesq model[J].Coastal Engineering, 1999, 37(1):57-96 [17]郑永红，沈永明，吴修广，等.用改进的Boussinesq方程模拟潜堤上的波浪变形[J]. 中国工程科学，2004，(04): 34-40. [18]ZHENG Y H, SHEN Y M, WU X G, et al.Simulation of Wave Propagation Over a Submerged Bar Using a Modified Boussinesq Equation[J]. Strategic Study of CAE, 2004, (04): 34-40. (in Chinese) [19]BEJI S, NADAOKA K.A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth[J].Ocean Engineering, 1996, 23(8):691-704 [20]MADSEN P A, SCH?FFER H A.Higher-Order Boussinesq-Type Equations for Surface Gravity Waves: Derivation and Analysis[J].Philosophical Transactions Mathematical Physical & Engineering Sciences, 1998, 356(1749):3123-3184 [21]ZOU Z L, FANG K Z.Alternative forms of the higher-order Boussinesq equations: Derivations and validations[J].Coastal Engineering, 2008, 55(6):506-521 [22]LIU Z B, FANG K Z.Two-layer Boussinesq models for coastal water waves[J]. Wave Motion, 2015, 57:88-111. [23]刘忠波，邹志利，王诺.四阶Boussinesq模型验证及非线性精度对数值结果的影响[J]. 海洋通报, ，2008，(05): 1-7. [24]LIU Z B, ZOU Z L, WANG N.Validation of a Fourth Order Boussinesq Model and the Effect of Nonlinearity Accuracy on Numerical Results[J]. Marine Science Bulletin, 2008, (05): 1-7. (in Chinese) [25]LIU Z B, FANG K Z, SUN J W.A multi-layer Boussinesq-type model with second-order spatial derivatives:Theoretical analysis and numerical implementation[J]. Ocean Engineering, 2019, 191 :106545. [26]邹志利，张晓莉.高阶水波方程数值模型及其与实验结果的对比[J].水动力学研究与进展辑, 2002, 17(5):592-603 [27]ZOU Z L, ZHANG X L.Numerical model of higher-order Boussinesq equations and comparisons with laboratory measurements[J].Chinese Journal of Hydrodynamics, 2002, 17(5):592-603 [28]ZOU Z L, LIU Z B, FANG K Z.Further improvements to the higher-order Boussinesq equations: Bragg reflection[J].Coastal Engineering, 2009, 56(5-6):672-687 [29]HSIAO S C, LYNETT P, HWUNG H H, et al.Numerical Simulations of Nonlinear Short Waves Using a Multilayer Model[J].Journal of Engineering Mechanics, 2005, 131(3):231-243 [30]WILMOTT C J.On the validation of models[J].Physical Geography, 1981, 2(2):219-232
