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

被引:2
作者
Yin Jing [1 ,2 ]
Sun Jia-wen [1 ,2 ]
Wang Xing-gang [2 ,3 ]
Yu Yong-hai [1 ]
Sun Zhao-chen [2 ]
机构
[1] Natl Marine Environm Monitoring Ctr, Dalian 116023, Peoples R China
[2] Dalian Univ Technol, Key State Lab Coastal & Offshore Engn, Dalian 116023, Peoples R China
[3] Nanjing Hydraul Res Inst, Nanjing 210029, Jiangsu, Peoples R China
关键词
non-hydrostatic model; shock-capturing; wave breaking; finite volume method; MUSTA scheme; FREE-SURFACE FLOW; EFFICIENT COMPUTATION; SHALLOW FLOWS; WAVE; ZONE; ALGORITHM; BREAKING; SWASH; RUNUP; DRY;
D O I
10.1007/s13344-017-0031-4
中图分类号
TU [建筑科学];
学科分类号
0813 ;
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.
引用
收藏
页码:261 / 271
页数:11
相关论文
共 50 条
[41]   Central WENO hybrid schemes used in the finite-volume method [J].
Fan, Jinzhi ;
Li, Hua .
Guofang Keji Daxue Xuebao/Journal of National University of Defense Technology, 2014, 36 (03) :6-13
[42]   A Finite-Volume Model for Numerical Solidification of Mg Alloys [J].
Farrokhnejad, Mehdi ;
Straatman, Anthony ;
Wood, Jeffrey .
LIGHT METALS TECHNOLOGY 2013, 2013, 765 :281-285
[43]   A non-negative and high-resolution finite volume method for the depth-integrated solute transport equation using an unstructured triangular mesh [J].
Ronghui Ye ;
Chenming Zhang ;
Jun Kong ;
Guangqiu Jin ;
Hongjun Zhao ;
Zhiyao Song ;
Ling Li .
Environmental Fluid Mechanics, 2018, 18 :1379-1411
[44]   A non-negative and high-resolution finite volume method for the depth-integrated solute transport equation using an unstructured triangular mesh [J].
Ye, Ronghui ;
Zhang, Chenming ;
Kong, Jun ;
Jin, Guangqiu ;
Zhao, Hongjun ;
Song, Zhiyao ;
Li, Ling .
ENVIRONMENTAL FLUID MECHANICS, 2018, 18 (06) :1379-1411
[45]   A 2DH fully dispersive and weakly nonlinear Boussinesq-type model based on a finite-volume and finite-difference TVD-type scheme [J].
Liu, Weijie ;
Ning, Yue ;
Shi, Fengyan ;
Sun, Zhilin .
OCEAN MODELLING, 2020, 147
[46]   Convergence of a Finite-Volume Scheme for a Heat Equation with a Multiplicative Stochastic Force [J].
Bauzet, Caroline ;
Nabet, Flore .
FINITE VOLUMES FOR COMPLEX APPLICATIONS IX-METHODS, THEORETICAL ASPECTS, EXAMPLES, FVCA 9, 2020, 323 :275-283
[47]   Finite-volume scheme for a degenerate cross-diffusion model motivated from ion transport [J].
Cances, Clement ;
Chainais-Hillairet, Claire ;
Gerstenmayer, Anita ;
Juengel, Ansgar .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (02) :545-575
[48]   Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise [J].
Bauzet, Caroline ;
Nabet, Flore ;
Schmitz, Kerstin ;
Zimmermann, Aleksandra .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2023, 57 (02) :745-783
[49]   Fitted finite volume positive difference scheme for a stationary model of air pollution [J].
Chernogorova, Tatiana ;
Vulkov, Lubin .
NUMERICAL ALGORITHMS, 2015, 70 (01) :171-189
[50]   Fitted finite volume positive difference scheme for a stationary model of air pollution [J].
Tatiana Chernogorova ;
Lubin Lubin Vulkov .
Numerical Algorithms, 2015, 70 :171-189