I am working on my Thesis (Bachelorarbeit), and I am having trouble solving a simple equation, because of the non symmetric advective matrix.
My thesis is about a 2-D pollution transport system without diffusion.
The transport equation is:
dc/dt=-v*∇C
After applying Galerkin Method, using nodes in the vertex of a rectangle.
The weak form, at the end is
[M]*C°+[K]*C=0,
where C° = dc/dt.
K = Advective Matrix.
M = Mass Matrix.
C= Concentration
For example, for one Dimension , [K ]is
K = U/2* [-1 1
-1 1]
After global assembling of my system, the result are zeros in the diagonal, and there is nothing that i can do. to find the Concentration in the unknown nodes.
I have read a lot about stabilization methods, like Petrov Galerkin or Artificial Diffusion, but all require a little of Diffusion, specifically to determine the Peclet Number (Pe), but i have none Diffusion.
I hope someone can help me, how to proceed.
Greetings from Chile
Juan Ignacio Correa.