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

• Published in: Computer physics communications Vol. 181; no. 12; pp. 2008 - 2023
• Main Authors: Ryan, Emily M., Tartakovsky, Alexandre M., Amon, Cristina
• Format: Journal Article
• Language: English
• Published: United States Elsevier B.V 01.12.2010
• 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; Flux; Smoothed particle hydrodynamics; Boundary conditions; Reactive transport; Surface reactions
• ISSN: 0010-4655; 1064-8275; 1879-2944; 1095-7197
• DOI: 10.1016/j.cpc.2010.08.022

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.