1. Introduction to MT3DMS All equations & illustrations taken
from the MT3DMS manual

2. Refer to the document on the course homepage entitled
“MT3DMS Solution Methods and Parameter Options”
(Look under the MT3DMS tab on the homepage)

3. General form of the ADE:
Expands to 9 terms
Expands to 3 terms
(See eqn in Z&B)

4. 9 Dispersion
Coefficients

5. This schematic assumes that

6. MODFLOW MT3DMS MT3DMS time steps are selected by the code considering
stability constraints, if any, and Courant numbers.

9. Dispersion, sink/source, chemical reactions
Advection

10.  

11. MT3DMS Solution Options1 2 3 4

12. j-1 j
j+1 x
j-1/2
j+1/2

13. Upstream weighting
Central differences

14. MT3DMS Solution Options

15. Explicit Approximation

16. Stability constraints for explicit solutions
Courant Number
Stability constraints
for explicit solutions

17. Courant Number 6 Courant Numbers Cr < 1 One for each face of
the cell block

18. MT3DMS Solution Options
Use GCG Solver

20. Implicit Approximation
for advection term

22. MT3DMS Solution Options 

23. a higher order FD method
TVD ULTIMATE METHOD
a higher order FD method
Conventional FD methods
use 3 nodes in the FD
approximation. The TVD
method uses 4 nodes with
upstream weighting. This
essentially eliminates
numerical dispersion.

24. Steps in the TVD Method Check for oscillation errors oscillation
Correction
for oscillation
errors

25. TVD ULTIMATE METHOD In one dimension Compare with an equation for a
lower order explicit approximation

26. MT3DMS Solution Options  

27. Eulerian vs Lagrangian Methods
Eulerian: fixed coordinate system with mass flux
through an REV
Lagrangian: moving particles; each particle carries mass.
The Random Walk method is a Lagrangian method.
Mixed Eulerian-Lagrangian methods use particles to solve
the advection portion of the ADE and an Eulerian method
to solve the rest of the equation.

28. Method of Characteristics
(MOC)
where  is a weighting factor to weight concentration between time level n and an intermediate time level n*, normally
 = 0.5 2 3 1 4
Step 1 is a Lagrangian method;
Step 3 is a Eulerian method.
Also update concentration of each particle. For example,
for particles in cell m:

29. MOC uses multiple particles per cell.
MMOC uses one particle per cell.
HMOC uses multiple particles in high concentration regions
and one particle per cell elsewhere.

30. Dynamic Particle Allocation

31. Breakthrough curve for example problem
in the MT3DMS manual
Compare with Fig in Z&B

33. MT3DMS Solution Options
PS#2 1 3 4 2