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

Abstract

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.

The Impact of Injection/Pumping Wells on the Pollution Transport in Groundwater

“…A mixed Eulerian-Lagrangian approach is used by the MT3D model to solve the advective-dispersive-reactive equation. This can be done depending on the supposition that concentration changes cannot influence the flow field significantly [30]. The model uses a modular structure like that implemented in the U.S. Geological Survey (USGS) modular three-dimensional finitedifference groundwater flow model, referred to as MODFLOW [31][32][33].…”

The Modified Eulerian-Lagrangian Formulation for Cauchy Boundary Condition Under Dispersion Dominated Flow Regimes: A Novel Numerical Approach and its Implication on Radioactive Nuclide Migration or Solute Transport in the Subsurface Environment

“…Hence, it can be expected that the numerical error may propagate and may be accumulated on the Cauchy boundary condition in a dispersion dominated regime (Suk, 2015).…”