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solve partial differential equation

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Gravel

solve partial differential equation

Hi,

         I am trying to solve the Kynch sedimentation process. For that, I need some help solving PDE with certain initial and boundary conditions. The objective is to get volume fraction (ϕ) in terms of height (z) and time (t). I am not really sure on how to go about doing this. It would be helpful if someone could take a look at it.

 

Thanks.

17 REPLIES 17

Re: solve partial differential equation

You appear to be using phi as a variable and as a function at the same time.

LM_20190207_PDEsolve.png

That is begging for trouble. You have to clear this up before you can begin to solve.

 

Success!
Luc

 

Re: solve partial differential equation

Hi,

       I have followed the equations given in the paper. Kindly check the attachments. 

Re: solve partial differential equation

To my opinion the paper uses inconsistent formulation.

At one time f is a function of just phi: "f(phi)".

At another point it is a function of two variables: "f(0,t)".

Mathcad, nor Prime will be able to work with that.

 

Success!
Luc

 

P.S

In your usage of Prime, with the derivative, you can leave the 'order' of the derivative blank if it's just 1 (It's only needed for second and higher order derivatives). That 'll help with readability.

 

Re: solve partial differential equation

Hi,

           Since df(ϕ)/dϕ=V, can I just put V*dϕ/dz instead for the second part of the equation. Will that help? Other than that, I am not really sure on how to proceed.

 

Regards

Re: solve partial differential equation

I think that would help.

Now go and look up the information on 'PDEsolve' in het Prime help and apply it to your system.

Don't hesitate to come back here (with an attached Prime sheet) if you run into trouble.

{I don't have full Prime, 'cause I never wanted to pay for it; hence I'm limited to 'Express', which doesn't do PDEsolve. But I can view your files with no problem.}

 

Success!
Luc

Re: solve partial differential equation

PDESolve is part of real Mathcad (that is version 15 and below) for a long time, but as far as I know its not implemented in Prime.

In Prime concerning PDEs we are restricted to the use of the command line solvers.

"numol" for hyperbolic and parabolic PDEs and "multigrid"/"relax" for elliptic ones.

 

Re: solve partial differential equation

I thought I'd better try is symbolically...:

LM_20190209_PDEsolve.png

So we have an expression for the function phi.

Now from here you should be able to solve the two remaining constants a[0 & a[1 and subsequently find out if this function describes the behaviour you're looking for.

 

Success!
Luc.

Re: solve partial differential equation

Hi,

Below are my attempts to find a particular solution, using MAthcad 15, to the equation, after having defined the boundary condition for ϕ:

arnair81.jpg

Re: solve partial differential equation

Hi LucMeekes,

        Sorry for not being able to reply a little sooner. I am a little confused by how you got square of d/dz ϕ(z,t,V,a) in the pde. Shouldn't it just be d/dz ϕ(z,t,V,a) as per the original equation. Kindly clarify. I think I follow the rest.

 

Also, my guess is your soln is in mathcad 15 and not prime. Any ideas on how to transfer it into prime 4. 

 

Regards