Mathematical model whit implicit method and Finite differences

I need to model this equation, tried model it severy times but i dont get the answer, i just need the model

$\varnothing \frac{\partial \rho }{\partial t}+\nabla(\rho u)=q; u=-\frac{k}{\mu } (\nabla p-\rho g\nabla z) $

  • Savionf Savionf
    +1

    Questions at this level should definitely come with a fair bounty, otherwise you may not get a response.

  • M F H M F H
    0

    What do you mean by "model"? These are n+1 partial differential equations (when grad & u have n components). You can only solve it if you have q & rho & z and boundary conditions given. Also, there's a weird character (symbol of empty set) in front of the equation. I guess that should be ignored? Anyway, clarify "model".

    • M F H M F H
      0

      * read "have q & p & z given", not rho, that's one of the unknown functions (the n other ones are the components of u) which you can compute if you have the initial / boundary values. There are many different methods, but essentially you'll have to discretize in time and space.

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