A well-balanced and positivity-preserving SPH method for shallow water flows in open channels

Kao Hua Chang, Tsang Jung Chang, Marcelo H. Garcia

Research output: Contribution to journalArticlepeer-review


A well-balanced and positivity-preserving meshless method based on smoothed particle hydrodynamics (SPH) is developed to simulate one-dimensional (1D) and two-dimensional (2D) shallow water (SW) flows in open channels with irregular geometries. A new form of the characteristic equations that govern the water-surface level and water velocity is introduced to specify the numerical inflow/outflow boundary conditions. An additional condition, derived from temporal discretization to determine the time-step size, forces the water depth to be positive. A 1D finite volume shallow water (FVSW) model based on the first-order Godunov upwind method is built to conduct a comparison of the 1D meshless-based and mesh-based SW models. Six benchmark cases–still water, single trapezoidal and rectangular and prismatic and non-prismatic channels, and a dendritic channel network–are employed to validate the proposed models and compared with the exact and mesh-based numerical solutions. A real-world case of the Chicago Area Waterways System (CAWS) is investigated to highlight the performance of the proposed 1D model for a practical hydraulic system.

Original languageEnglish (US)
Pages (from-to)903-916
Number of pages14
JournalJournal of Hydraulic Research
Issue number6
StatePublished - 2021


  • CAWS
  • positivity-preserving
  • shallow water
  • smoothed particle hydrodynamics
  • well-balanced

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology


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