Boundary layer — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
Also named here as streamline diffusion — the same set of essays touches all of them, so they are one junction rather than several.
The diffusion that makes the answer exact
Upwinding adds h/2 of artificial diffusion. Central differencing adds none. Add ε·ξ·Pe with ξ = coth(Pe) − 1/Pe and the computed solution is the exact one at every grid point, to 2.4·10⁻¹⁷ — at every Péclet number, on the problem it was derived from and on no other.
Exact along one axis
The tuned diffusion makes the answer exact at every node, and in two dimensions it holds at exactly one flow angle. Five degrees off the grid the relative error goes from 1.2·10⁻¹⁴ to 6.9, and by twenty degrees the scheme is worse than the upwinding it was built to improve on.
The direction the diffusion does not go
Streamline diffusion adds τbbᵀ, a rank-one tensor that annihilates every direction across the flow. That is the design. The price is 18, 50 and 48 nodes where the computed solution leaves the interval the equation guarantees — and half a coefficient of crosswind diffusion halves the error at every angle while costing exactly nothing where the scheme was exact.
Named alongside it
The objects these essays reach for when they reach for this one.
Artificial diffusionConvection diffusionPeclet numberStreamline diffusionGrid alignmentM matrixManufactured solutionUpwindingAnisotropyCrosswind diffusionDiscrete maximum principleDiscretisation error