Non-negative numerical solutions of the two-dimensional full-tensor diffusion/dispersion problems using flux-corrected transport, and implementation for the groundwater transport simulator MT3DMS

Yan, Shuo

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Description

Title

Non-negative numerical solutions of the two-dimensional full-tensor diffusion/dispersion problems using flux-corrected transport, and implementation for the groundwater transport simulator MT3DMS

Author(s)

Yan, Shuo

Issue Date

2019-04-24

Director of Research (if dissertation) or Advisor (if thesis)

Valocchi, Albert J.

Department of Study

Civil & Environmental Eng

Discipline

Environ Engr in Civil Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

1. Groundwater transport simulation 2. Full-tensor dispersion 3. Non-negative solutions 4. Flux corrected transport 5. MT3DMS 6. MODFLOW

Abstract

Solute transport model in groundwater system is usually represented by the advection-dispersion-reaction equation. When standard numerical methods are used to solve this solute transport equation, there can be non-physical overshoot and undershoot behavior. Several studies have shown that cross-terms in a dispersion tensor can lead to undershoots. These cross-terms arise whenever the principal directions of dispersion are not aligned with a fixed coordinate system. Since the principal directions are aligned with the direction of groundwater flow, full tensor dispersion must be included for realistic groundwater transport problems. The problem of unphysical undershoots caused by dispersion cross-term cannot be ignored, considering that concentration of contaminants can never be negative in a groundwater system. In addition, negative solutions in dispersion cross-term can create artificial mass, cause numerical convergence problems and result in unstable results in a reactive transport model. To address these issues, this thesis applies the well-known flux corrected transport (FCT) technique to various numerical methods, including standard finite volume, standard continuous Galerkin finite element and a bilinear finite volume method. FCT algorithm is easy to construct, and it only requires operation on matrices for the final system of linear algebraic equations. In this methodology, the low order transport operator is initially constructed from the high order transport operator by inserting an artificial operator to eliminate troublesome off-diagonal components. The anti-diffusive fluxes with a flux limiter are then added into the low order scheme (low accuracy but positive solution) to construct a high-order and physical solution. Considering the flexibility and accuracy of FCT algorithm, I implement this algorithm in the well-known and widely used groundwater solute transport simulator, MT3DMS. A new solute simulator, MT3DMS-FCT, is developed to guarantee the positivity of the transport solution. MT3DMS-FCT is developed to demonstrate feasibility of implementing FCT into an existing production code; the current implementation is limited to nonreactive species, use of operator splitting to separately solve the advection and dispersion terms, and Dirichlet boundary conditions. In this thesis, the accuracy and numerical performance of various FCT schemes are tested for several benchmark problems. The results indicate that FCT algorithm is high spatial order, robust and flexible method to guarantee the positivity of solution for solute transport model. However, the FCT results for standard finite volume method is very sensitive to the time step size. Moreover, while FCT guarantees a non-negative solution, it may not eliminate all numerical oscillations. The numerical behavior and accuracy of MT3DMS-FCT are compared to that of MT3DMS by using different test problems. More importantly, FCT algorithm is successfully implemented in the existing solute transport simulator MT3DMS, which lays out the implementation work for other simulators.

Graduation Semester

2019-05

Type of Resource

text

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Copyright and License Information

2019 by Shuo Yan. All rights reserved.

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