Contaminant and sediment transport by advection and diffusion 213
the same way as it would be quantified by solving the transport equation.
The concentration in each cell of the discretization grid can be easily measured from the number of particles (representing defined volume or mass of
the substance) contained within the specific cell.
For accuracy, this technique requires a large number of tracked particles,
so that the concentration in each cell is approximated by a sufficient number of them. In the case of a non-conservative substance, the decomposition
or decay of the mass is simulated by removing particles from the moving
cluster of particles. The number of particles removed at each time step Δt is
related to the decay coefficient λ and the number of the tracked particles as
N removed = N total λ Δt
(8.19)
This Lagrangian particle-tracking method can be applied for the simulation of
either a sudden accidental contaminant release or for a continuous pollution
source discharging in receiving waters. In the first case all particles are placed
in a specific ‘source’ location x o , y o at t = 0. In the second case, a predefined
number of new particles are placed at the source location at each time step.
Example 8.3
This application involves the simulation of a contaminant advection and diffusion using a Lagrangian particle-tracking method. The
bathymetry, velocity field and location of the contaminant source are
the same to the ones in Example 8.1. The source is simulated by 5000
particles introduced at time t = 0. The simulation was conducted for
a period of 720 time steps (1 hour) and the results are illustrated in
Figure 8.5. The similarities between the results of the particle tracking
40
35
30
25
20
15
10
5
10
20
30
40
50
60
70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 8.5 Simulation of mass transport using the particle-tracking method.
the same way as it would be quantified by solving the transport equation.
The concentration in each cell of the discretization grid can be easily measured from the number of particles (representing defined volume or mass of
the substance) contained within the specific cell.
For accuracy, this technique requires a large number of tracked particles,
so that the concentration in each cell is approximated by a sufficient number of them. In the case of a non-conservative substance, the decomposition
or decay of the mass is simulated by removing particles from the moving
cluster of particles. The number of particles removed at each time step Δt is
related to the decay coefficient λ and the number of the tracked particles as
N removed = N total λ Δt
(8.19)
This Lagrangian particle-tracking method can be applied for the simulation of
either a sudden accidental contaminant release or for a continuous pollution
source discharging in receiving waters. In the first case all particles are placed
in a specific ‘source’ location x o , y o at t = 0. In the second case, a predefined
number of new particles are placed at the source location at each time step.
Example 8.3
This application involves the simulation of a contaminant advection and diffusion using a Lagrangian particle-tracking method. The
bathymetry, velocity field and location of the contaminant source are
the same to the ones in Example 8.1. The source is simulated by 5000
particles introduced at time t = 0. The simulation was conducted for
a period of 720 time steps (1 hour) and the results are illustrated in
Figure 8.5. The similarities between the results of the particle tracking
40
35
30
25
20
15
10
5
10
20
30
40
50
60
70
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 8.5 Simulation of mass transport using the particle-tracking method.