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

Authors:
Todd Arbogast;Chieh-Sen Huang
Affiliations:
The University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX 78712, USA and The University of Texas at Austin, Institute for Computational Engineering and S ...;Department of Applied Mathematics and National Center for Theoretical Sciences, National Sun Yat-sen University, Kaohsiung 804, Taiwan, ROC
Venue:
Journal of Computational Physics
Year:
2010

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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.