What is it?
MT3D is a modular three-dimensional (3-D) transport model originally developed by Zheng (1990) at S. S. Papadopulos & Associates, Inc. It was later updated (MT3DMS) at The University of Alabama for the U.S. Department of Defense (Zheng and Wang 1999), and most recently modified and updated by the U.S. Geological Survey (MT3D-USGS) (Bedekar and others 2016). MT3D is widely used to simulate advection, dispersion, and chemical reactions of contaminants in groundwater. IGW-NET provides the user with the option to use MT3D-USGS to solve contaminant fate and transport equations resulting from discretization of the conceptual model.Additionally, when using IGW-NET to model density-dependent flows (with SEAWAT), the MT3D solver interface inputs will be used internally.
MT3D solver inputs are dependent on the advection solver used; if no changes are made, default values will be used. Parameter lookup tables may be helpful for users familiar with MT3D variable names.
Note: MODFLOW-like boundary condition packages explicitly integrated with MT3D-USGS in the IGW-NET platform include:
- Recharge (RCH)
- Well (WEL)
- Drain (DRN)
- General Head Boundary(GHB)
- River (RIV)
Future integration planned for the additional packages:
- Lake (LAK)
- Stream Flow (SFR)
Realtime MT3D-USGS in MAGENT supports both default IGW-NET and MODFLOW groundwater flow solvers (see notes below)
Advection Solver
These parameters control the advection (flow) parameters of the MT3D solver, or the component of transport that results from groundwater flow rather than dispersion of diffusion.Note: In the IGW-NET implementation, particle positions are not saved between timesteps. Thus the user may wish to run longer IGW-NET transport timesteps, or use a finer grid if using the forward tracking MOC or HMOC methods, as numerical dispersion is introduced when multiple concurrent steps are evaluated. Additionally, if the grid is coarse, or the timestep is short (relative to the groundwater velocity and the number of particles assigned to each cell), particles may become "trapped" leading to errant results.
- Advection Solver: Here select the scheme used to solve advective chemical transport.
'FDM' is the standard finite-difference method and is well suited for obtaining first approximations in the initial stages of modeling. FDM is computationally efficient and evaluates interface concentrations using either the upstream or the central-in-space weighting scheme. Because these schemes have problems with numerical dispersion or artificial oscillation, FDM is best used for transport models not dominated by advection (i.e., do not use when either the physical dispersivity is small or the grid resolution is too coarse).
'MOC' is the forward tracking Method of Characteristics. The MOC technique is nearly free of numerical dispersion caused by spatial truncation errors, but, especially in 3-D, can be slow and require significant computer memory when tracking many particles. The MOC technique can also have mass balance discrepancies due to the discrete nature of the particle-tracking-based mixed Eulerian-Lagrangian solution.
'MMOC' is the Modified or backward tracking Method of Characteristics. This solution is computationally efficient but has significant numerical dispersion and is not intended for advection dominated problems with sharp concentration fronts.
'HMOC' the Hybrid Method of Characteristics automatically and dynamically selects the MOC or MMOC schemes depending on concentration gradients. The MOC technique is used to solve the advection term for sharp concentration fronts (steeper than the specified concentration gradient threshold) while the MMOC technique is used elsewhere.
'ULTIMATE' the third-order total-variation-diminishing (TVD) scheme determines concentrations through a third-order polynomial interpolation of nodal concentrations, supplemented by a universal flux limiting procedure to minimize unphysical oscillations from sharp concentration fronts. This scheme is mass conservative and does not introduce excessive numerical dispersion or artificial oscillation but may be computationally intensive. [default 'MMOC'].
- Stability/Courant number [decimal]: The number of cells, or a fraction of a cell advection will be allowed in any direction in one MT3D substep. [default 0.75; range 1e-5 to ~1]. For accuracy reasons, it should generally not be set much greater than one.
- FDM weighting scheme: (finite difference; FDM) The method used by the FDM solver.
The 'upstream' weighting scheme uses upstream concentrations and results in oscillation-free solutions, however, is only accurate to the first order, leading to numerical dispersion for advection dominated problems (truncation error from the advection solution can overwhelm the physical dispersion term).
The 'central-in-space' weighting scheme calculates concentrations from weighted averages (equivalent to linear interpolation), and is accurate to the second order. While this solution is without numerical dispersion it can develop artificial oscillation (typical of higher-order truncation errors) for advection dominated transport problems.
- Particle tracking method: (MOC/MMOC/HMOC schemes) Here select the method used to track particles.
The '1st-order Euler' algorithm moves particles based on previous positions and velocities. This works well in uniform flow, but may be inaccurate for particles in strongly converging or diverging flows (near sources or sinks) unless the MT3D substep is very small.
The '4th-order Runge-Kutta' algorithm evaluates the velocity four times for each MT3D substep and then uses a weighted velocity based on these values to move particles. This is more accurate than the Euler algorithm and permits larger MT3D substep, but at the cost of additional computational effort making it less efficient for 3-D simulations with many particles.
The 'Hybrid' method, uses the Euler algorithm in regular cells, and the Runge-Kutta algorithm in sink/source and adjacent cells, and is a compromise between computation and accuracy [default 'Hybrid'].
- Conc weighting factor [decimal]: used for operator splitting in the particle-tracking-based methods. This value can be increased to achieve better mass balance as advection becomes more dominant [default 0.5; range 0.5 - 1.0]
- Max # particles: (forward tracking; MOC/HMOC) The maximum number of particles allowed in a cell.
- Advective Conc gradient threshold [decimal]: (forward tracking; MOC/HMOC) The threshold used below to determine the number of particles per cell.
- Number of planes: (forward tracking; MOC/HMOC) The number of horizonal planes in which particles are placed. A random configuration is generally sufficient, but the number can be explicitly increased to obtain better vertical resolution for 3-D simulations.
- Particles per cell:
- below conc gradient [integer]: (forward tracking; MOC/HMOC schemes) The number of particles placed in cells with concentrations less than the specified threshold.
- above conc gradient [integer]: (forward tracking; MOC/HMOC schemes) The number of particles placed in cells with concentrations greater than the specified threshold.
- minimum number [integer]: (forward tracking; MOC/HMOC schemes) The minimum number of particles allowed in a cell.
- maximum number [integer]: (forward tracking; MOC/HMOC schemes) The maximum number of particles allowed in a cell.
- sink cell particles [integer]: (backward tracking; MMOC/HMOC schemes) The number of particles placed in a sink cell (like a well or drain).
- Number of planes for sinks: (backward tracking; MMOC/HMOC schemes) The number of horizonal planes in which sink particles are placed. A random configuration is generally sufficient, but the number can be explicitly increased to obtain better vertical resolution for 3-D simulations.
- Conc gradient threshold for HMOC [decimal]: (HMOC scheme) the relative concentration gradient threshold for the hybrid solution to choose between the MOC or MMOC techniques. [default 0.0001]
Basic Transport Parameters
- Route mass through dry cells (for MODFLOW-NWT)[checkbox]: (finite difference or TVD; FDM/ULTIMATE schemes) Check to enable mass transfer through dry cells, when dry cells can remain active in a flow simulation, as is possible with MODFLOW-NWT. May improve mass balance for some models [default unchecked]- Only use saturated cell portion for sorbing [checkbox]: Uncheck to use the old MT3DMS formulation whereby the entire cell thickness is available for solid-aqueous phase interactions (even for partially saturated cells). Default (checked) only the saturated portion of the cell is available for sorbing.
- Min sat. thickness [decimal]: The minimum saturated thickness for transport (as a fraction of layer thickness) [default 0.01; range 0-1]
- Initial MT3D substep length [decimal]: The initial transport substep MT3D; if 0 is used MT3D will calculate substep size based on the Courant number/stability constraints specified above. [default 0; auto calculate]
- Max # of MT3D substeps [integer]: MT3D will stop if more than this number of steps are required to meet stability criteria within a transport timestep. [default 5000]
- MT3D substep length multiplyer [decimal]: (finite difference; FDM scheme) This multiplyer may improve speed by increasing the length of substeps as transport progresses. [default 1.0 (constant substep length); range 1.0-2.0]
- Max MT3D substep length [decimal]: (finite difference; FDM scheme) The maximum length of an MT3D substep when the substep length multiplyer is greater than one. Zero can be used to indicate no limit on substep length [default 0].
Generalized Conjugate Gradient Parameters
These parameters control the GCG package that iteratively solves the system of transport equations. Dispersion, sink/source, and reaction terms are solved implicitly without any stability constraints. The advection term is solved using the scheme chosen above. Eulerian-Lagrangian methods- Max number of iterations
- Outer loop [integer]: max number of outer iterations; use 1 unless a nonlinear sorption isotherm is used [default 1].
- Inner loop [integer]: max number of inner iterations; 30-50 should be adequate for most problems [default 50]
- Preconditioner for Lanczos/ORTHOMIN Acceleration Scheme: The Modified Incomplete Cholesky (MIC) preconditioner typically converges faster, but requires more memory than the Jacobi or SSOR preconditioners [default MIC preconditioner]. For the SSOR option a relaxation factor of 1.0 is generally adequate [default is 1].
- For dispersion tensor: Choose how to handle dispersion tensor cross terms. Lumping all dispersion cross terms to the right-hand-side is approximate but computationally efficient. Including the full dispersion tensor may be more accurate but is memory intensive. Ignoring cross terms may be beneficial to avoid erroneous negative concentrations for some problems [default lump to right-hand-side].
- Convergence criteria [decimal]: Determines the level of accuracy required from the iterative solver (in terms of relative concentration). A value between 1e-4 and 1e-6 is generally adequate. [default 1e-5]
External Links
- MT3D FloPy documentation.
- MT3D-USGS
Landing page for MT3D-USGS
MT3D-USGS manual - Bedekar and others (2016)
- MT3DMS (version 5.2 utilized implicitly when running variable density models with SEAWAT)
Documentation landing page - University of Alabama Hydrogeology Group
MT3DMS user manual - Zheng & Wang (1999)
MT3DMS v5 supplemental documentation - Zheng (2010)