Refer to the document on the course homepage entitled
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Transcript of Refer to the document on the course homepage entitled
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Refer to the document onthe course homepage entitled
“MT3DMS Solution Methods and Parameter Options”
(Look under the MT3DMS tab on the homepage)
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Dispersion, sink/source, chemical reactions
Advection
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MT3DMS Solution Options
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MT3DMS Solution Options
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Stability constraintsfor explicit solutions
Courant Number
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MT3DMS Solution Options
Use GCG Solver
Use GCG Solver
Use GCG Solver
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MT3DMS Solution Options
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TVD ULTIMATE METHODa higher order FD method
Conventional FD methodsuse 3 nodes in the FDapproximation. The TVDmethod uses 4 nodes withupstream weighting. Thisessentially eliminatesnumerical dispersion.
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Steps in the TVD Method
Correctionfor oscillationerrors
Check foroscillationerrors
oscillation
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TVD ULTIMATE METHOD
In one dimension
Compare with an equation for alower order explicit approximation
nj
nj
nj
nj ccc
x
tvc
)( 1
1
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MT3DMS Solution Options
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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.
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Method of Characteristics(MOC)
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where is a weighting factor to weight concentration between time level n and an intermediate time level n*, normally = 0.5
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1*1 nm
nm
nm CCC4Step 1 is a Lagrangian method;
Step 3 is a Eulerian method.
Also update concentration of each particle. For example,
for particles in cell m:11 n
mnp
np CCC
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• 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.
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Dynamic Particle Allocation
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Breakthrough curve for example problemin the MT3DMS manual
Compare with Fig. 7.26 in Z&B
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Time (years)
Co
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TVD
HMOC
Upstream weighting
Central FD
Upstream FD
Central FD
TVD
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MT3DMS Solution Options
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PS#2