numerical diffusion in 1D
 

Hey everyone,

I am wondering something about numerical diffusion - I have a 3D finite volume code that uses the power law discretization for velocity and central differencing for diffusion. For time stepping, I am marching with rk4.

As a test case, I have given an initial gaussian along the channel, but with uniform concentration across the channel and no flux boundary conditions across the channel. In other words, a 3D code that has been made 1D for testing purposes. My question is this - Should I expect to see any numerical diffusion? I know that upwinding causes it, and I believe that power law does as well because it too is first order. However, I thought that it only appeared when the flow is diagonal to the grid. I have simply given an axial velocity of 1, and diffusion=0, to see if I can make this gaussian advect. It does, but it also diffuses. The code is perfectly conservative, so I don't think losing concentration to the walls is the problem.

Should I expect this? Any possible solutions that would still allow me to keep my power law scheme?

Thanks! Jon

Re: numerical diffusion in 1D
 

I think numerical diffusion is possible in multidimensional problems only.

Re: numerical diffusion in 1D
 

Numerical diffusion can and does occur in 1D. If you look at all the classic mathematical descriptions, the analyses are almost always 1D.