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An efficient operator splitting scheme for three‐dimensional hydrodynamic computations
Author(s) -
Lu Qimiao,
Wai Onyx W. H.
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19980415)26:7<771::aid-fld672>3.0.co;2-7
Subject(s) - discretization , mathematics , finite element method , computation , eulerian path , operator (biology) , numerical diffusion , numerical analysis , total variation diminishing , mathematical analysis , stability (learning theory) , mechanics , physics , lagrangian , algorithm , computer science , biochemistry , chemistry , repressor , machine learning , gene , transcription factor , thermodynamics
A new efficient numerical method for three‐dimensional hydrodynamic computations is presented and discussed in this paper. The method is based on the operator splitting method and combined with Eulerian–Lagrangian method, finite element method and finite difference method. To increase the efficiency and stability of the numerical solutions, the operator splitting method is employed to partition the momentum equations into three parts, according to physical phenomena. A time step is divided into three time substeps. In the first substep, advection and Coriolis force are solved using the explicit Eulerian–Lagrangian method. In the second substep, horizontal diffusion is approximated by implicit FEM in each horizontal layer. In the last substep, the continuity equation is solved by implicit FEM, and vertical diffusion and pressure gradient are discretized by implicit FDM in each nodal column. The stability analysis shows that this method is unconditionally stable. A number of numerical experiments have been performed. The results simulated by the present scheme agree well with analytical solutions and the other documented model results. The method is efficient for 3D shallow water flow computations and fully fits complicated configurations. © 1998 John Wiley & Sons, Ltd.