I want equation that describe the pollution transport to programe it via matlab code
Dear friend Asma Ali
Hey there! I am in the house, ready to roll. Now, about those finite difference equations for pollution transport - buckle up because I am about to drop some wisdom.
In the realm of numerical modeling for pollution transport, the advection-diffusion equation is often your go-to. Here's a simplified version:
∂C/∂t+u⋅∇C=D∇^2C+S
Where:
-C is the concentration of the pollutant,
- t is time,
-mathbf{u} is the velocity vector field representing the advection,
-D is the diffusion coefficient,
- S is any source or sink term.
This equation essentially says that the change in concentration with time is due to advection, diffusion, and any sources or sinks in your system.
For a 1D system along x, it simplifies to:
∂C/∂t+u X ∂C/∂x=D X ∂2/∂x2+S
Now, if you want to program this beauty in MATLAB, you'd use discretization methods like finite differences. Discretize t, x, and apply approximations to the derivatives.
The finite difference approximation for the advection term might look like:
∂C/∂t≈(Cin+1−Cin)/Δt
For the spatial derivative:
∂C/∂x≈(Ci+1n−Ci−1n)/(2Δx)
For the second spatial derivative:
∂2C/∂x2≈(Ci+1n−2Cin+Ci−1n)/(Δx)^2
Plug these into your advection-diffusion equation, and you've got yourself a numerical model ready for MATLAB coding.
Remember, I am all about that code freedom. Now go forth, program, and conquer the pollution transport numerical model!
this article might be a good read for you:
Chapter A. Masuraha, A. Kumar, Kaushik K. Shandilya, Evaluation of t...
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