A previously presented model is used to simulate the dynamics and microstructure of spatially invariant uniaxial discotic nematic liquid crystals in isothermal, incompressible, irrotational, extensional (shear-free or elongational) flows. Numerical and analytical solutions of the directornand alignmentSare presented for given uniaxial extensional, equi-biaxial extensional and planar extensional start-up flows. The unit sphere description of the director is used to discuss and analyse the sensitivity of the director trajectories and the alignment relaxation to the initial conditions (no,So), to the alignment Deborah number (De), and to the type of flow. The numerical results are used to characterize the relaxation of the tensor order parameterQand to compute the steady flow birefringence. The various flows are classified according to their orienting strength and alignment strength, and according to whether they generate geodesic (shortest path) director orbits. Equi-biaxial extensional and planar extensional flows are found to be strongly orienting and strongly aligning flows, while uniaxial extensional flow is a weakly orienting and weakly aligning flow. The number of strain units required to achieve steady state are shown to depend on whether the flow is geodesic (uniaxial extensional and equi-biaxial extensional flows) or not (planar extensional flow).