# One dimentional problems(flow) in CFD

1. Oct 7, 2008

### mahaesh

Hi everyone

My question is
What is the meaning of one dimentional problem(flow)? Can one dimentional problem(flow) solve in CFD? If the answer is yes then How?

2. Oct 7, 2008

### minger

Any 1-D flow is simply flow where the variables only change in one direction. Look at the common Couette Flow, which is typically used to introduce analytic solutions to the Navier-Stokes Equations.

In this flow, the fluid starts at rest between two plates. At t=0, the top plate moves at a velocity U. If you assume that the plate is infinitely deep and long, then the flow only changes in the vertical direction between the plates.

From another standpoint, one can look at the General Heat Equation, which I believe looks something like:

$$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} +\frac{\partial^2 T}{\partial z^2} = \frac{1}{\alpha}\frac{\partial T}{\partial t}$$

If you consider a case like a flat wall, i.e. a very tall wall in your house. You can assume that there is no change in the vertical direction and no change "into the page." If you then assume that the solutions is steady state, you're left with the much simpler equation:

$$\frac{\partial^2 T}{\partial x^2} =0$$

1D CFD solvers can't typically solve much though. I the flow is 1D, then the geometry must also be 1D. That means essentially you have a long staight tube. Nothing really happens.

With that said, a 1D solver for the wave equation is extremely useful in learning how spatial and time derivatives behave. I have written one, and I can probably assume most people who have studied it have as well.

Beyond that, one can write a pseudo-2D code, which at that point can be extremely cool. A code like this solves the equations in 1D, but then adds a source term which simulations a change in area. My old CFDII final was this project. The area was in such a way that it simulated a choked nozzle. The results were perfect.