中文摘要：

波浪破碎是海岸工程所关注的关键水动力学问题之一,而波浪破碎的数值模拟技术的研究方兴未艾。高效的浅水方程基于静压假定,而通过引入动压项建立的完全非静压模型,可成功应用于色散水波的模拟。自由表面的捕捉采用的垂向坐标变换技术,较之VOF（Volume of Fluid）模型,计算效率较高。但垂向坐标变换不能模拟大曲率自由表面变形,即波浪破碎过程。对于破碎波的模拟,一种高效的模式分裂法应用至非静压模型,即在波浪破碎局部水域将模型分裂为静压模型和非静压模型,破碎波波峰附近退化至静压模型,并持续至波浪破碎结束再恢复为动压模型。通过典型算例,验证了模式分裂法的适用性及对于波浪破碎过程的模拟精度,鉴于模式分裂法对于波浪破碎过程的模拟未引入新的概化模型,计算效率较高,可应用于大尺度的海岸带波浪的变形、破碎及越浪的数值模拟。

英文摘要：

Wave breaking is one of the key hydrodynamic issues in coastal engineering, and the research on numerical simulations of wave breaking is in the ascendant. Based on the static pressure model, a completely non-hy- drostatic model is proposed by introducing the dynamic pressure term and has been successfully applied to the simula- tion of dispersive water waves. Vertical coordinate transformation approach is adopted to capture the free water surface, which exhibits improved computationally efficiency as compared to the conventional VOF method. However, the verti- cal coordinate transformation approach cannot simulate large-curvature free surface deformation, i. e., the wave break- ing process. Therefore, a model-splitting method is developed to simulate breaking waves, in which the model in the wave breaking zone is divided into a hydrostatic model and a non-hydrostatic model. That is, near the peaks of break- ing waves the model is degraded to the hydrostatic model, which persists until the end of wave breaking and thereafter reverts to the dynamic pressure model. In this paper, the applicability of the model-splitting method and its accuracy for the simulation of wave breaking process are validated against canonical cases. Since this method has not introduced any new generalized model for wave breaking process, it has high computational efficiency and can be applied to the simulation of large-scale wave deformation, fragmentation and propagation in the coastal zone.