Integral approximations to classical diffusion and smoothed particle hydrodynamics
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. An immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 1182873
- Report Number(s):
- PNNL-SA-107015; KJ0401000
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, 286:216-229, Journal Name: Computer Methods in Applied Mechanics and Engineering, 286:216-229
- Country of Publication:
- United States
- Language:
- English
Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media
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