A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization

Tian, Hao; Ju, Lili; Du, Qiang

doi:10.1016/j.cma.2017.03.020

A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization

Journal Article · Wed Mar 22 00:00:00 UTC 2017 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2017.03.020· OSTI ID:1533652

Tian, Hao ^[1]; Ju, Lili ^[2]; Du, Qiang ^[3]

Ocean University of China, Qingdao (China); DOE/OSTI
University of South Carolina, Columbia, SC (United States)
Columbia University, New York, NY (United States)

Here in this paper, we first propose a nonlocal convection–diffusion model, in which the convection term is constructed in a special upwind manner so that mass conservation and maximum principle are maintained in any space dimension. The well-posedness of the proposed nonlocal model and its convergence to the classical local convection–diffusion model are established. A quadrature-based finite difference discretization is then developed to numerically solve the nonlocal problem and it is shown to be consistent and unconditionally stable. We further demonstrate that the numerical scheme is asymptotically compatible, that is, the approximate solutions converge to the exact solution of the corresponding local problem when δ → 0 and h → 0. Numerical experiments are also performed to complement the theoretical analysis.

View Accepted Manuscript (DOE)

Research Organization:: University of South Carolina, Columbia, SC (United States)

Sponsoring Organization:: Air Force Office of Scientific Research (AFOSR); Army Research Office (ARO); Central Universities; National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0008087; SC0016540

OSTI ID:: 1533652

Alternate ID(s):: OSTI ID: 1550578

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 320; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
97 MATHEMATICS AND COMPUTING
asymptotically compatible
mass conservation
maximum principle
nonlocal convection–diffusion
quadrature-based finite difference

A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization

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