Wrong sign in upwinding detection with particular coefficient form

[isaacsas]

See Discourse, feel free to close if this is not an error: https://discourse.julialang.org/t/stability-issue-with-methodoflines/84133/5

[xtalax]

Seems to boil down to this:

Yes good go ahead:

eq = Dτ(g(τ, x)) ~ - λ * (x - xb) * Dx(g(τ, x)) 

No stop bad:

eq = Dτ(g(τ, x)) ~ λ * (xb - x) * Dx(g(τ, x)) 

A head scratcher to be sure, as the values of - λ * (x - xb) and λ * (xb - x) should be known, concrete and equal at discretization time.