A parallel unstructured finite volume method (FVM) is developed and implemented under a distributed computing environment through the parallel virtual machine (PVM) libraries, and is used to simulate the channel flow of the Oldroyd-B fluid past a circular cylinder. Differing from our previous work [11,12], a discrete elastic viscous split stress (DEVSS) formulation together with an independent interpolation of the vorticity (DEVSS-omega) is proposed in this paper. This method has almost the same stability behavior as the elastic viscous split stress (EVSS) formulation, and is suitable for complex constitutive models. To further improve the stability at high Deborah numbers, we combine the idea of the discrete adaptive elastic viscous split stress (DAVSS) formulation [7] with the independent interpolation of the vorticity to arrive at the DAVSS-omega method. The numerical implementation is based on the unstructured FVM method and the semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm. The parallelization of die program is implemented by a domain decomposition strategy and using PVM software libraries. The results are compared with those by the EVSS, DEVSS, and the plain Oldroyd-B formulation (without splitting the stress). It is found that the drag coefficient first decreases and then increases with the De number, for a channel half width to cylinder radius ratio of h/R = 2. It is also confirmed that the drag enhancement at high Deborah number is due to the increasing extension effect in the regions near the front and the rear stagnation points.