TY - JOUR
T1 - A fully conservative Eulerian–Lagrangian method for a convection–diffusion problem in a solenoidal field
AU - Arbogast, Todd
AU - Huang, Chieh-Sen
N1 - KAUST Repository Item: Exported on 2020-10-01
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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2010/5
Y1 - 2010/5
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/597274
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999110000240
UR - http://www.scopus.com/inward/record.url?scp=77949319472&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2010.01.009
DO - 10.1016/j.jcp.2010.01.009
M3 - Article
SN - 0021-9991
VL - 229
SP - 3415
EP - 3427
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 9
ER -