A finite analytic method for solving the 2-D time-dependent advection–diffusion equation with time-invariant coefficients

Lowry, Thomas Stephen; Li, Shu Guang

doi:10.1016/j.advwatres.2004.10.005

Cited by 10 publications

(1 citation statement)

References 41 publications

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“…However, the ELMs, including the Neuman approach, LEZOOMPC, as well as the MOC, MMOC, and HMOC included in MT3DMS have been applied mainly under a Dirichlet boundary condition, with few exceptions (Neuman , ; Konikow et al ; Cheng et al ; Lowry and Li ; Herrera et al ). However, in the field, it would rarely be realistic to apply the Dirichlet boundary condition, because it is rare that the concentration of a source at a point will remain fixed in time regardless of changes in the accompanying flow field or in the local concentration gradient (Konikow ).…”

Section: Introductionmentioning

confidence: 99%

Modified Mixed Lagrangian–Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary

Suk

2016

Groundwater

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MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes.

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