- #1

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## Main Question or Discussion Point

Well, I was solving the 3D diffusion equation:

##\displaystyle \frac{1}{c}\frac{\partial \phi(\mathbf{r},t)}{\partial t}-D\nabla^2 \phi(\mathbf{r},t)=q(\mathbf{r},t)##.

I wrote a program to do this. The problem concerns the diffusion of light. However, all this time I've been working with nondimensional units. I have set c=1, and solved everything that way, for different values of D.

In real problems, c is the speed of light, which is a huge number (##299 792 458 m / s##), and D is given in centimeters, typical values are around 0.3 cm to 0.01cm. The thing is that D is usually a small number, and c is huge. Should I expect to have some numerical problems when I solve this numerically? whatever I do with the dimensional units, there is no way I can avoid this huge difference of magnitudes, I think I should write everything in centimeters, which is the usual laboratory dimension concerning this type of experiments, or would it be better just to set c=1?

If I choose c=1, that fixes a ratio of space/time, so I'm not sure what should I do with the other variables, basically I'm saying that ##299 792 458 m / s=1##.

I am solving this using a forward Euler scheme in time.

##\displaystyle \frac{1}{c}\frac{\partial \phi(\mathbf{r},t)}{\partial t}-D\nabla^2 \phi(\mathbf{r},t)=q(\mathbf{r},t)##.

I wrote a program to do this. The problem concerns the diffusion of light. However, all this time I've been working with nondimensional units. I have set c=1, and solved everything that way, for different values of D.

In real problems, c is the speed of light, which is a huge number (##299 792 458 m / s##), and D is given in centimeters, typical values are around 0.3 cm to 0.01cm. The thing is that D is usually a small number, and c is huge. Should I expect to have some numerical problems when I solve this numerically? whatever I do with the dimensional units, there is no way I can avoid this huge difference of magnitudes, I think I should write everything in centimeters, which is the usual laboratory dimension concerning this type of experiments, or would it be better just to set c=1?

If I choose c=1, that fixes a ratio of space/time, so I'm not sure what should I do with the other variables, basically I'm saying that ##299 792 458 m / s=1##.

I am solving this using a forward Euler scheme in time.