Upwind differencing — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The stencil that is not symmetric
Past a cell Péclet number of exactly one — measured by bisection at 1.0000000000000002 — the central-difference solution of a convection–diffusion problem oscillates from point to point and leaves the interval the equation guarantees, at 16 of 31 grid points. It is the exact solution of its own linear system, to 4.6·10⁻¹⁸. No solver was involved.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
Artificial diffusionConvection diffusionM matrixPeclet numberBoundary layerDiscretisationDiscretisation errorManufactured solutionNon symmetric operatorSmoothing factorStreamline diffusion