A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

作者：Yin Jing; Sun Jia-wen^*; Wang Xing-gang; Yu Yong-hai; Sun Zhao-chen

来源：China Ocean Engineering, 2017, 31(3): 261-271.

DOI：10.1007/s13344-017-0031-4

• non-hydrostatic model
• shock-capturing
• wave breaking
• finite volume method
• MUSTA scheme

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

• 出版日期2017-6
• 单位大连理工大学; 国家海洋环境监测中心; 水利部交通运输部国家能源局南京水利科学研究院