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Introduction to MT3DMS

Introduction to MT3DMS. All equations & illustrations taken from the MT3DMS manual. Refer to the document on the course homepage entitled “MT3DMS Solution Methods and Parameter Options” (Look under the MT3DMS tab on the homepage). General form of the ADE:. Expands to 9 terms.

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Introduction to MT3DMS

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  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. 3.48 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.

  7. Dispersion, sink/source, chemical reactions Advection

  9. 1 2 3 4 MT3DMS Solution Options

  10. x j j+1 j-1 j-1/2 j+1/2

  11. Upstream weighting Central differences

  12. MT3DMS Solution Options

  13. Explicit Approximation

  14. Courant Number Stability constraints for explicit solutions

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

  16. Use GCG Solver Use GCG Solver Use GCG Solver MT3DMS Solution Options

  17. Implicit Approximation for advection term

  18. MT3DMS Solution Options  

  19. 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.

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

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

  22. MT3DMS Solution Options   

  23. 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.

  24. 2 where  is a weighting factor to weight concentration between time level n and an intermediate time level n*, normally  = 0.5 3 4 1 Also update concentration of each particle. For example, for particles in cell m: Method of Characteristics (MOC) Step 1 is a Lagrangian method; Step 3 is a Eulerian method.

  25. 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.

  26. Dynamic Particle Allocation

  27. Breakthrough curve for example problem in the MT3DMS manual Compare with Fig. 7.26 in Z&B

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

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