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

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 m...

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Bibliographic Details
Published in:Computer physics communications 2010-12, Vol.181 (12), p.2008-2023
Main Authors: Ryan, Emily M., Tartakovsky, Alexandre M., Amon, Cristina
Format: Article
Language:English
Subjects:
Boundaries
BOUNDARY CONDITIONS
Computational fluid dynamics
Computer simulation
COMPUTERIZED SIMULATION
DIFFUSION
Fluid flow
Flux
HYDRODYNAMICS
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical models
PARTICLES
Reactive transport
Smoothed particle hydrodynamics
SPH, reactive transport, flux, boundary conditions, computational modeling
SURFACE FORCES
SURFACE PROPERTIES
Surface reactions
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Summary: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.
ISSN:0010-4655
1064-8275
1879-2944
1095-7197
DOI:10.1016/j.cpc.2010.08.022