You need more than some code.
The equations you are interested in are differential equations. I think they are partial differential equations instead of ordinary ones.
Finding solutions to such equations requires a lot more than writing some code. It requires writing a lot of code, usually after doing some high level analysis.
Since Fluid dynamics is a well reseached field, you might find help in a good math library. There might be some internet sites with articles.
The big problem you have is lack of sufficient background. You are likely to have trouble understanding the books/articles you find.
A typical math major takes some elementary and advanced calculus courses, which deal briefly with differential equations. Then he takes a course in ordinary differential equations. Finally, he might take a course in partial differential equations.
Some math majors might go off in other directions and not take any courses in differential equaitons other than the intorductory work in a calculus course.
At any rate, such subject matter is beyond the scope of this forum.
I have done a lot of work with the ordinary differential equations used for gravitaional computations, so I am probably way ahead of you in back ground knowledge. I would not be able to cope with the equations you provided without spending quite a few hours researching the subject matter and getting my self up to speed in this area.