Recent content by vector_problems

I am trying to solve the poisson equation with neumann BC's in a 2D cartesian geometry as part of a Navier-Stokes solver routine and was hoping for some help. I am using a fast Fourier transform in the x direction and a finite difference scheme in the y. This means the poisson equation becomes...

sorry, should have been more clear. u_x is the partial derivative of u w.r.t. x and i am trying to solve for u, du/dx=(sin(x))*(u)

Does anyone know if it is possible to solve an equation of the type u_x=(sin(x))*(u) on a periodic domain using the fft. I have tried methods using convolutions but have had no success thanks in advance

ok that's great, thank you very much for your help

so if i had a more general point in cartesian co-ordinates; p_cart=(px,py,pz) to express this in a cylindrical geometry do I just do p_polar=(sqrt(px^2+py^2),arctan(py/px),pz) or will I need a transformation matrix in this case thanks

from the picture it would seem that p_polar=(r,theta,z)=(1,pi/2/0) but this just seems too simple. I would have thought i would have needed to use some sort of transformation matrix to transform from cartesian to polar e.g. p_r=cos(theta)p_x+sin(theta)p_y, p_theta=-sin(theta)p_x+cos(theta)p_y...

thank you very much for the welcome :) just to clarify in case this changes things. The vector i am working with is a direction vector rather than a position vector. i.e. it describes the orientation of a particle with preferred orientation (0,1,0). Will the same theory apply, thanks for the...

thank you

Hi, I was wondering if anyone could help with a vector question that I have. If I have a unit vector defined in cartesian co-ordinates as p= (0,1,0) how would I go about converting this vector to a cylindrical geometry. I understand that I will probably need to use p_r=sqrt(px^2+py^2) and...