On discrete time schemes for the problem of fibre suspension flows

Abstract

We present a time discrete stability results presented in [9], we use the tools presented in [3,6] to show that the results obtained in [9] can be generalized to obtain estimates not only for the velocity but also for the orientation tensor and a non zero body force, and without decomposing the orientation tensor into a sum of diagonal and a traceless tensors.  As for the regular solutions, we prove the solutions of a discrete scheme are continuously dependent on the initial data and the same body force.  Also, the restrictions imposed on the data con rm a well known result proven in [4, 8, 9], that for the rest state to be stable, the particle number Np must be less than 35/2.