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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| Published in | Computer physics communications Vol. 181; no. 12; pp. 2008 - 2023 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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United States
Elsevier B.V
01.12.2010
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| Abstract | 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. |
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| AbstractList | In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries. The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions. 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. |
| Author | Tartakovsky, Alexandre M. Ryan, Emily M. Amon, Cristina |
| Author_xml | – sequence: 1 givenname: Emily M. surname: Ryan fullname: Ryan, Emily M. email: emily.ryan@pnl.gov organization: Carnegie Mellon University, Department of Mechanical Engineering, Scaife Hall, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA – sequence: 2 givenname: Alexandre M. surname: Tartakovsky fullname: Tartakovsky, Alexandre M. email: alexandre.tartakovsky@pnl.gov organization: Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352, USA – sequence: 3 givenname: Cristina surname: Amon fullname: Amon, Cristina email: dean@ecf.utoronto.ca organization: Carnegie Mellon University, Department of Mechanical Engineering, Scaife Hall, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA |
| BackLink | https://www.osti.gov/biblio/1000607$$D View this record in Osti.gov |
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| Keywords | Flux Smoothed particle hydrodynamics Boundary conditions Reactive transport Surface reactions |
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| Snippet | We present a novel smoothed particle hydrodynamics (SPH) method for diffusion equations subject to Neumann and Robin boundary conditions. The Neumann and Robin... In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin... |
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| StartPage | 2008 |
| SubjectTerms | 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 |
| Title | A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics |
| URI | https://dx.doi.org/10.1016/j.cpc.2010.08.022 https://www.proquest.com/docview/1770357464 https://www.proquest.com/docview/831187724 https://www.osti.gov/biblio/1000607 |
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