@Rouben Rostamian  

Hi again! Function f(x,y) is the radial velocity in cylindrical corrdinates, so it is a perpendicular ray from axis z to a point in the cylinder.  

 

@Rouben Rostamian  

Hi again Rouben! 

1. We are working in cylindrical coordinates.

2. The delta function in the second initial condition is due to the gradient of the pressure that appears in the Navier-Stokes equation. In our case x=1 is the tornado's wall. Because of the difference in pressure inside and outside the tornado, the pressure has a heaviside function in it, so its derivate is delta funcion.  

3. For being able to get an equation for radial velocity out of 4 equations (which usually describe fluid dynamics) we had to get the derivate of two of these equations so their  second partial derivates would be the same. 

4. The delta function in the equation means there is an explosion at the moment t = 0, and it occurs in the axis of the tornado 0<x<0.1 (lets say 10 % of the tornado's radius), so it is described by Heaviside, but again for the same reason as in the third point, we got its derivate 

Thanks again for taking your time on helping me, I really appreciate it.

Oscar

@Rouben Rostamian  

Hi Rouben! No, the equation is alright, I know that it looks almost like the laplacian in polar coordinates but that is how it should be. Maybe it would be good  to use narrow gaussian functions instead of delta functions? How good does Maple work with delta functions? Also I was thinking about how to change the mesh or the spatial coordinate step size...

Hi guys! Thank you so much for taking the time on helping me with this.  My phD tutor and I are solving the fluid dynamics equations for a tornado in which an explosion in its axis occurs. We have an analytical solution and I also made the model in Comsol but the radial velocity of these solutions isnt exactly the same. So now Im trying to get the numerical solution in Maple. In the equations x is the dimensionless radius and y is the dimensionless time. From the initial conditions for a statical tornado ( pressure and velocity) we get the second initial condition for x and y=0. The first initial condition means there is no radial velocity component at the begining. The third means that the velocity at x=0 is always 0. ( the fourth condition in fact is wrong - now Im using f(1000,y) = 0 so the radial velocity far away from the tornado is also cero always. With these condition I get some numeric answer but when I try to plot the answer I get an error for y > 0 . So Im getting no answer anyway ... 

Maybe you have any ideas !)