On the principal axes of diffusion in difference schemes for 2D transport problems (Q920597)

With the operator \(Lu:=au_ x+bu_ y\) the 9-point box type finite difference operator \(L^ hu=Lu+h/2\{Au_{xx}+2Bu_{xy}+Cu_{yy}\}+O(h^ 2)\) is associated. By rotating axes to eliminate the \(2Bu_{xy}\) term, the principle axes through which the diffusion in \(L^ h\) acts is calculated. It is shown for many schemes for 2D transport problems that these axes have little to do with the ``streamline'' and ``crosswind'' directions of the continuous problem. Several examples are discussed.