NUMERICAL METHOD FOR POLLUTANT TRANSPORT
Pollutant transport phenomenon has been a concerning problem in our efforts to preserve the environment. Mathematically, this phenomenon is usually portrayed by the advection diffusion equation which is derived from Fick’s first law and the continuation equation. In this study, the mathematical m...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/54851 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Pollutant transport phenomenon has been a concerning problem in our efforts
to preserve the environment. Mathematically, this phenomenon is usually portrayed
by the advection diffusion equation which is derived from Fick’s first law and the
continuation equation. In this study, the mathematical model is observed in one and
two dimensions which is then solved using four different numerical methods. We
use the 2nd, 4th and 6th order Forward Time Centered Space and Forward Time
Backwards Space Centered Space to solve the mathematical methods. Later, this
study further examines the methods by determining the stability conditions,
consistency and the order of accuracy by using the Von Neumann stability analysis
and Taylor series. To follow that, we confirm each method and its properties by
comparing the numerical results with an existing analytical problems and solutions.
From those experiments, we can conclude that every method is able to represent the
analytical solution. However, in each dimension and each method possesses
different stability conditions and orders of accuracy. In obtaining this result, we
believe that this study could illustrate the pollutant transport phenomenon. |
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