haitrungdo82: My thinking was very vague. We know 0.5*(f_t,x+1 - f_t,x-1)/deltax is the first-order finite difference approximation of the first derivative, if I recall correctly. And v*deltat is an x (horizontal) distance. Therefore, this horizontal distance times the above-mentioned first derivative (which would be the tangent of the slope angle) should be a vertical (y) distance, if I recall correctly.
We know (f_t,x-1 - 2*f_t,x + f_t,x+1)/deltax^2 is the first-order finite central difference approximation of the second derivative (curvature), if I recall correctly. Therefore, similarly, when we multiply this value times D*deltat, we get another y distance. I do not recall the exact details.
Therefore, I vaguely envisioned that if we supply a D value too large or too small, the equation was overshooting below y = 0, or overshooting in the horizontal direction (?), which, in either case, would give garbage. I envisioned that if D is too small, it has no effect on the dispersion. If D is too large, the equation overshoots. I envisioned if deltax is too small, we get almost a singularity, called overflow. We want to increase D, but I envisioned that we cannot increase it too much unless we decrease deltat; otherwise, the problem will overshoot, as explained above. I envisioned that you cannot decrease deltat below a certain value, or else the problem will crash or overshoot. And I envisioned that you cannot decrease deltax below a certain value, or else the problem will crash or overshoot. E.g., if we want to simulate out to 10 km, it seems deltat cannot be less than 0.5 s, and deltax cannot be less than ~8 m. I do not understand very well what was going on, nor how to control the diffusion equation. If you uncover anything else, feel free to let us know.
I had to increase D seemingly too much (?); but that is the only way I could get the problem to run. In your given problem, D is overpowered by the relatively high wind velocity.
In the "Graph from Question" file, we see a lot of diffusion, and almost no wind. We can see that the centerline of the probability density moves slightly in the negative x direction, which means there is a very, very slight wind in the negative x direction.
By the way, to reply to a post, did you know you can just press the "New Reply" button? You don't need to press the "Quote" button on every reply. Also, always leave a space between a numeric value and its following unit symbol. E.g., 10 km, not 10km. See the
international standard for writing units[/color] (
ISO 31-0[/color]).
If you uncover anything else, feel free to let us know.