Hi, I'm trying to solve a time dependent advection-diffusion equation with periodic boundary conditions. Just a simple du/dt = D \nabla^2 u - v \dot \grad u for now. I use a large diffusion constant, so stability shouldn't be an issue. The solution behaves normally in the bulk, but some of the mass gets reflected once the mass gets to a boundary. The total mass (integral of u over space) then decreases each time it goes through the boundary in one direction, and increases if the velocity is set to go the other way. Any idea why this might be the case? The periodic boundary works fine when its just diffusion and no advection.
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