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Refer to the document on the course homepage entitled

Refer to the document on the course homepage entitled “MT3DMS Solution Methods and Parameter Options” (Look under the MT3DMS tab on the homepage). Dispersion, sink/source, chemical reactions. Advection. 1. 2. 3. 4. MT3DMS Solution Options. MT3DMS Solution Options. Courant Number.

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Refer to the document on the course homepage entitled

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

  2. Dispersion, sink/source, chemical reactions Advection

  3. 1 2 3 4 MT3DMS Solution Options

  4. MT3DMS Solution Options

  5. Courant Number Stability constraints for explicit solutions

  6. Use GCG Solver Use GCG Solver Use GCG Solver MT3DMS Solution Options

  7. MT3DMS Solution Options  

  8. 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.

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

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

  11. MT3DMS Solution Options   

  12. 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.

  13. 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.

  14. 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.

  15. Dynamic Particle Allocation

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

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

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