Refer to the document on the course homepage entitled “MT3DMS Solution Methods and Parameter...
19
Refer to the document on the course homepage entitled T3DMS Solution Methods and Parameter Options (Look under the MT3DMS tab on the homepage)
-
date post
19-Dec-2015 -
Category
Documents
-
view
218 -
download
4
Transcript of Refer to the document on the course homepage entitled “MT3DMS Solution Methods and Parameter...
Refer to the document onthe course homepage entitled
“MT3DMS Solution Methods and Parameter Options”
(Look under the MT3DMS tab on the homepage)
Dispersion, sink/source, chemical reactions
Advection
MT3DMS Solution Options
1
2
3
4
MT3DMS Solution Options
Stability constraintsfor explicit solutions
Courant Number
MT3DMS Solution Options
Use GCG Solver
Use GCG Solver
Use GCG Solver
MT3DMS Solution Options
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.
Steps in the TVD Method
Correctionfor oscillationerrors
Check foroscillationerrors
oscillation
TVD ULTIMATE METHOD
In one dimension
Compare with an equation for alower order explicit approximation
nj
nj
nj
nj ccc
x
tvc
)( 1
1
MT3DMS Solution Options
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.
Method of Characteristics(MOC)
1
where is a weighting factor to weight concentration between time level n and an intermediate time level n*, normally = 0.5
2
3
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
• 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.
Dynamic Particle Allocation
Breakthrough curve for example problemin the MT3DMS manual
Compare with Fig. 7.26 in Z&B
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Time (years)
Co
nce
ntr
atio
n
TVD
HMOC
Upstream weighting
Central FD
Upstream FD
Central FD
TVD
MT3DMS Solution Options
1
2
3
4
PS#2
