  We study the switching dynamics in two-domain and four-domain twisted nematic
liquid crystal devices. The equilibrium configuration of these devices involves
the coexistence of regions characterised by different handedness of the
inherent director twist. At the boundaries between these regions there are
typically disclinations lines. The dynamics of the disclination lines controls
the properties, and in particular the switching speed, of the devices. We
describe their motion using a numerical solution of the Beris-Edwards equations
of liquid crystal hydrodynamics. Hence we are able to explain why a
conventional two-domain device switches off slowly and to propose a device
design which circumvents this problem. We also explain the patterns of
disclination creation and annihilation that lead to switching in the
four-domain twisted nematic device.
