A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics

Emily M. Ryan, Alexandre M. Tartakovsky, Cristina Amon

Research output: Contribution to journalArticlepeer-review


We present a novel smoothed particle hydrodynamics (SPH) method for diffusion equations subject to Neumann and Robin boundary conditions. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to implement in numerical methods when the boundary geometry is complex. The new method presented here is based on the approximation of the sharp boundary with a diffuse interface and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method. The paper discusses the details of the method and the criteria for the width of the diffuse interface. The method is used to simulate diffusion and reactions in a domain bounded by two concentric circles and reactive flow between two parallel plates and its accuracy is demonstrated through comparison with analytical and finite difference solutions. To further illustrate the capabilities of the model, a reactive flow in a porous medium was simulated and good convergence properties of the model are demonstrated.

Original languageEnglish (US)
Pages (from-to)2008-2023
Number of pages16
JournalComputer Physics Communications
Issue number12
StatePublished - Dec 2010
Externally publishedYes


  • Boundary conditions
  • Flux
  • Reactive transport
  • Smoothed particle hydrodynamics
  • Surface reactions

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)


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