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H
holti1-Visitor
1-Visitor
September 18, 2020
Question

Solving ODE with 2 independant variables

  • September 18, 2020
  • 11 replies
  • 6812 views

Hello,

 

I'm trying to solve an ODE of 2nd Degree (Couette flow):

 

0 = eta * d²u/dy² + dp/dx

This works out well with the common ODE solver from MathCad as Long as I determin a function for p as Long as:

u is a function of y  --> u=f(y)

and

p is a function of x --> p=f(x).

 

Along the x Axis my boundary conditions and my p(x) change so that "u" is no longer just a function just of y but also of x.

I implement this dependency by declaring my boundary conditions to be fuunctions of "x".

But in the end I cannot declare my "u" as a function of "y" and "x" because "y" is the only variable to be integrated over.

Please refer to the attached screenshots.

 

Thanks in Advance and greetings from Switzerland

11 replies

L
LucMeekes23-Emerald IV
23-Emerald IV
September 18, 2020

It will help if you attach the Prime worksheet.

To protect intellectual property, if necessary, limit the contents of that sheet to the bare minimum of your problem.

 

Success!
Luc

L
LucMeekes23-Emerald IV
23-Emerald IV
September 18, 2020

Seems like what you have is a Partial Differential Equation (or Boundary Value problem). For that you should need PDEsolve, not ODEsolve.

PDEsolve is (still) available in Mathcad 15, for which you have a license due to the fact that you're licensed to Prime (You can install and license Mathcad 15 using the very same license file that you used for Prime).

PTC did not (yet... will they ever?) include PDEsolve in Prime.

 

Success!
Luc

H
holti1-VisitorAuthor
1-Visitor
September 21, 2020

Hello LucMeekes,

 

thank You for this hint. I will ask my IT-Support to install MathCad 15.

A
AlanStevens19-Tanzanite
19-Tanzanite
September 18, 2020

I could be wrong, but doesn't this have the following solution:

g0.jpg

Correction: Penultimate line.  Where I wrote  if u(h,y) = 0 then ... I should have written  if u(x,h) = 0 then ...

 

 

Alan

W
WC_96380251-Visitor
1-Visitor
September 21, 2020
@AlanStevens wrote: upsers portal

I could be wrong, but doesn't this have the following solution:

g0.jpg

Correction: Penultimate line.  Where I wrote  if u(h,y) = 0 then ... I should have written  if u(x,h) = 0 then ...

 

 

Alan

Thanks for sharing useful information with us.. It really helpful to me..I always prefer to read the quality content and this thing I found in you post. thanks for sharing with us..

L
LucMeekes23-Emerald IV
23-Emerald IV
September 21, 2020

I think your answer should be found here: https://en.wikipedia.org/wiki/Couette_flow

If I use the solution to the PDE given there, I get:

LucMeekes_0-1600707096569.png

Success!
Luc

    A
    AlanStevens19-Tanzanite
    19-Tanzanite
    September 22, 2020

    Luc,  you've selected a solution to an equation with no dp/dx term.

     

    Alan

    L
    LucMeekes23-Emerald IV
    23-Emerald IV
    September 23, 2020

    I guess you are right.

    The OP stated he wants to solve a Cuette problem, so I looked it up and found this.

    If the problem really does involve two functions: u(y,...) and p(x,...), then a single (partial differential) equation will not do to find the two functions. A set of PDE's is needed. Or one of the two functions is known...

     

    Luc

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