Non-hydrostatic ocean models are widely required in coastal and estuarine studies but are limited in their application due to their very high computational expense. To alleviate this issue, this study developed a highly computationally efficient non-hydrostatic ocean model named MERF v3.0 (the third version of the Marine Environment Research and Forecasting model) in which a semi-implicit and variable layers (SIVL) scheme is proposed for dynamic pressure calculation. The SIVL scheme provides freedom to choose the ratio between the number of dynamic pressure layers and the number of velocity layers as required. Moreover, the model adopted numerical calculation framework OpenArray and PETSc (Portable, Extensible Toolkit for Scientific Computation) to achieve implicit parallelism and a concise code structure. Five classical numerical experiments were performed to validate the simulation capacity of this non-hydrostatic ocean model, including the standing wave in a closed basin, surface solitary wave, lock-exchange problem, periodic wave over a bar and tidally induced internal lee wave. The numerical simulation results are consistent with the analytical solutions and experimental data published in the literature. Benefitting from the advantages of OpenArray and PETSc, MERF v3.0 achieves an 87.8% parallel efficiency in the strong scaling test and an 84.1% parallel efficiency in the weak scaling test on 3584 processes, whereas the OpenArray limits the parallel efficiency of MERF v3.0 on more processes, which is beyond the scope of this article and will be further examined in our next study.

非静水力海洋模型在沿海和河口研究中被广泛需要，但由于计算成本非常高而在应用中受到限制。为了缓解这个问题，本研究开发了一种名为MERF v3.0（海洋环境研究和预测模型的第三版）的高计算效率的非静水力海洋模型，其中提出了半隐式和可变层（SIVL）方案用于动态压力计算。SIVL 方案提供了根据需要自由选择动态压力层数和速度层数之间的比率。此外，该模型采用数值计算框架OpenArray和PETSc（Portable, Extensible Toolkit for Scientific Computation）实现隐式并行和简洁的代码结构。进行了五个经典数值实验来验证该非静水力海洋模型的模​​拟能力，包括封闭盆地中的驻波、表面孤立波、锁交换问题、杆上的周期波和潮汐引起的内部背风波。数值模拟结果与文献中公开的解析解和实验数据一致。受益于OpenArray和PETSc的优势，MERF v3.0在3584个进程上实现了87.8%的强扩展测试并行效率和84.1%的弱扩展测试并行效率，而OpenArray限制了MERF v3的并行效率。 0 更多过程，这超出了本文的范围，将在我们的下一个研究中进一步研究。