  We study the Dean instability in curved channels using the lattice Boltzmann
model for generalized metrics. For this purpose, we first improve and validate
the method by measuring the critical Dean number at the transition from laminar
to vortex flow for a streamwise curved rectangular channel, obtaining very good
agreement with the literature values. Taking advantage of the easy
implementation of arbitrary metrics within our model, we study the fluid flow
through a double-curved channel, using ellipsoidal coordinates, and study the
transition to vortex flow in dependence of the two perpendicular curvature
radii of the channel. We observe not only transitions to 2-cell vortex flow,
but also to 4-cell and even 6-cell vortex flow, and we find that the critical
Dean number at the transition to 2-cell vortex flow exhibits a minimum when the
two curvature radii are approximately equal.
