A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field

Type
Article

Authors
Arbogast, Todd
Huang, Chieh-Sen

Date
2010-05

Abstract
Tracer transport is governed by a convection-diffusion problem modeling mass conservation of both tracer and ambient fluids. Numerical methods should be fully conservative, enforcing both conservation principles on the discrete level. Locally conservative characteristics methods conserve the mass of tracer, but may not conserve the mass of the ambient fluid. In a recent paper by the authors [T. Arbogast, C. Huang, A fully mass and volume conserving implementation of a characteristic method for transport problems, SIAM J. Sci. Comput. 28 (2006) 2001-2022], a fully conservative characteristic method, the Volume Corrected Characteristics Mixed Method (VCCMM), was introduced for potential flows. Here we extend and apply the method to problems with a solenoidal (i.e., divergence-free) flow field. The modification is a computationally inexpensive simplification of the original VCCMM, requiring a simple adjustment of trace-back regions in an element-by-element traversal of the domain. Our numerical results show that the method works well in practice, is less numerically diffuse than uncorrected characteristic methods, and can use up to at least about eight times the CFL limited time step. © 2010 Elsevier Inc.

Citation
Arbogast T, Huang C-S (2010) A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field. Journal of Computational Physics 229: 3415–3427. Available: http://dx.doi.org/10.1016/j.jcp.2010.01.009.

Acknowledgements
This author was supported in part by US National Science Foundation Grant DM5-0713815 and the King Abdullah University of Science and Technology (KAUST) Academic Excellence Alliance program.

Publisher
Elsevier BV

Journal
Journal of Computational Physics

DOI
10.1016/j.jcp.2010.01.009

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