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I wrote an excel VBA program that shows how a dye diffuses through water by taking one spreadhsheet cell and getting the average dye concentration for this cell and 8 of its immediate neighbours and repeating the procedure in a loop. Seems to work well. I am now doing this for weather prediction. How large are the errors likely to be in this procedure? It has the advantage that it only takes a couple of minutes to run the program. The photos below are symmetrical (have symmetrical values) as expected from putting dye in 4 corners in one and in the middle of the spreadsheet in the other.

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  • $\begingroup$ It doesn't look like there is enough information in the question to allow an answer. Unless someone reads the question who has accidentally done the same thing as you have, you will probably not get a useful answer. $\endgroup$
    – oliver
    Commented Mar 17, 2021 at 16:46
  • $\begingroup$ Sorry, what's VBA? $\endgroup$
    – AtmosphericPrisonEscape
    Commented Mar 17, 2021 at 17:32
  • $\begingroup$ Visual basic programming language $\endgroup$
    – user291777
    Commented Mar 17, 2021 at 18:31

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Simply, no. You have a model of a 2D diffusive process, but most flows are not dominated by diffusion. What weather phenomena are you hoping to model with this? There is a reason that one of the uses of supercomputers is for weather forecasting, the flow is incredibly complicated!

Atmospheric flows are typically turbulent, advection dominated and 3D, as well as having to consider buoyancy effects amongst other things. Perhaps with your Excel sheet you could examine the behaviour of the release of a neutrally buoyant pollutant on a very still day, but for anything else you would need to include a lot more physics. That's not to say it couldn't be done, I'm sure that with enough time and effort you could implement a Lattice Boltzman method in Excel, but I'm not sure why you would.

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You can't just jump from a diffusion problem for one variable and one equation to weather prediction.

As you aspire to do this in 2-D, you will already have to solve at least the mass, and two momentum equations simultaneously, together with the advection problem and pressure gradients. The mathematical character of your equations that you solve changes (from parabolic to hyperbolic), forcing you to use different techniques.

While you can do this in a naive way using finite differences (either using the isothermal equations or the shallow-water equations), you will miss out on a lot of physics. On the other hand, putting in more physics, you'll need significantly more equations and numerical methods than you probably have at hand right now.

Furthermore, doing this on a Excel sheet is not the tool you want to use. 9x9 cells is too small a resolution for just about any interesting effect to occur. Hence, this forces you to go to many more cells, at which point any scripted language will be painfully slow.

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