Recent content by bilgealp

Luke's variational principle is quite elegant and worth to mention especially when potential theory is on the scene. Even, variational calculus itself is a must for anyone interested in fluid mechanics. Finite element people are quite good at dealing with the variational form of the partial...

My pleasure.

I may suggest you think about a submerged rectangle first then a submerged prism and then convince yourself with a general shape. First Rule: In a fluid at rest, pressure at a point is equal to the height of the fluid body(h) * unit weight of the fluid, namely at point A, fluid pressure is...

OK. Both are different FD schemes of the problem. The first one is explicit in time* so you shoul be aware of the CFL condition that ensures stability. The other is the Crank-Nicholson type discretization which is stable but needs system solver. In this one you have to collect unknown...

This is a very simple problem in the area of heat conduction. There are several well written books in this area. However I have followed one of those best in the field. I will suggest Özışık (Ozisik for non-UTF viewers), M. Necati, "Heat Conduction", John-Wiley, 1993 and inquirer meant...

Okkey. Some more info on that. Assuming that you do not have constant diffusion coefficient, i.e. \kappa is inside the derivative with respect to z \frac{\partial}{\partial z}\left( \kappa \frac{\partial U}{\partial z} \right) then the best solution would be a staggered...

Hi chitambira, This is a very popular problem and a somewhat old paper using FD in 2-dimensions may help. Noye, B.J., Tan, H.H., "Finite Difference Methods for solving Two-Dimensional Advection-Diffusion Equation", International Journal For Numerical Methods in Fluids, vol.9, 75-98, 1989...

\operatorname{diag}(\lambda_1, \lambda_2, \cdots, \lambda_n) seems OK but does not look good in long equations. Some writers prefer to add a superscript D as in a^D. I always use small letters for vectors and capital letters for matrices. And if you combine this rule with the...

Thanks. Gilbert Strang rocks...