Grid alignment — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Also named here as upwinding — the same set of essays touches all of them, so they are one junction rather than several.
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 diffusionBoundary layerConvection diffusionPeclet numberStreamline diffusionUpwindingAnisotropyCrosswind diffusionDiscrete maximum principleM matrixManufactured solutionNodal exactness