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 

机构地区：[1]National Marine Environmental Monitoring Center, Dalian 116023, China [2]Key State Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China [3]Nanjing Hydraulic Research Institute, Nanjing 210029, China

出　　处：《China Ocean Engineering》2017年第3期261-271,共11页中国海洋工程（英文版）

基　　金：supported by the State Ocean Administration People’s Republic of China(Grant No.201405025);the Key Laboratory for Sea Area Management Technology(SOA)(Grant No.201603)

摘　　要：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.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.

关 键 词：non-hydrostatic model SHOCK-CAPTURING wave breaking finite volume method MUSTA scheme 

分 类 号：P731.2[天文地球—海洋科学] P75