Here, the oscillatory behavior of Saccharomyces cerevisiae (baker's yeast) was investigated during the operation of a continuous bioreactor as it is detrimental to the stability and productivity of such a system. An unstructured segregated model was employed to study this phenomenon. The mathematical model couples a biological cell population balance model (PBM), representing the dynamics of cell mass distribution, with the mass balance of the rate-limiting substrate. High resolution flux limiter finite volume schemes have been proposed for approximating model equations efficiently and accurately. Moreover, analytical solution of a simplified yeast cell PBM was derived and the accuracy of proposed numerical schemes was analyzed by comparing analytical and numerical solutions. Good agreements in results and error analysis proved the accuracy of the proposed numerical schemes. Finally, the Globally Linearizing Control (GLC) was used for obtaining the total cell mass per unit volume. The GLC damps oscillations in substrate concentration by controlling the total cell number per unit volume. The ability of this controller to stabilize the steady-state and periodic solutions was analyzed through numerical simulations.