In Fluid Dynamics we have to solve a system of PDE, some specific simplified formulation can reduce to ODE but generally FD method is used on the full PDE set.
You can read here an example of using MAPLE for that
Article Using symbolic computation software packages in production o...
The finite difference representation of the complete Navier-Stokes equations along with the continuity equation do indeed represent the fluid flow computational problem. I could readily produce this in Maple or FORTRAN or C, but it won't help you in the least. How you intend to solve the equations is the real problem and Maple isn't going to do that, even if given the correct equations. This is a huge topic and the subject of many textbooks and published articles. Setting up the equations, feeding in the boundary conditions, solving the equations, and viewing the results is the motivation for many very large commercial codes, such as Fluent. A significant percentage of the questions on RG are from people who are running fluid flow projects on these various codes. If you don't have access to one of these already mature CFD codes, there are a few available free on the web that can handle some classes of problems. If you're not using one of the mature extensive CFD codes, you must carefully match what you need it to do with which code you try to use. For instance, one may only work with open channel flows. while another will only work with aerodynamics (very high Reynolds numbers and gases), yet another will only work with creeping flow (very low Reynolds numbers).
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