An efficient operator splitting scheme for three-dimensional hydrodynamic computations

Qimiao Lu, Wing Hong Onyx Wai

Research output: Journal article publicationJournal articleAcademic researchpeer-review

24 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)771-789
Number of pages19
JournalInternational Journal for Numerical Methods in Fluids
Issue number7
Publication statusPublished - 15 Apr 1998


  • Eulerian-lagrangian method
  • Hybrid method
  • Shallow water equation
  • Sigma co-ordinate transformation
  • Splitting method
  • Three-dimensional numerical method

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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