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

I think numerical diffusion is possible in multidimensional problems only.

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