Integral approximations to classical diffusion and smoothed particle hydrodynamics [electronic resource].
- Washington, D.C. : United States. National Nuclear Security Administration, 2014.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy
- Physical Description:
- pages 216-229 : digital, PDF file
- Additional Creators:
- Sandia National Laboratories
United States. National Nuclear Security Administration
United States. Department of Energy. Office of Scientific and Technical Information
- The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.
- Published through SciTech Connect.
Computer Methods in Applied Mechanics and Engineering 286 C ISSN 0045-7825 AM
Qiang Du; R. B. Lehoucq; A. M. Tartakovsky.
- Funding Information:
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