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The paper deals with the simulation of batch crystallization processes and their crystal size distribution controllability by temperature control. The dynamic of crystallization processes under consideration is governed by hyperbolic partial differential equations. We propose simulating the processes of one size variable using the method of characteristics. It turns out that the method of characteristics has no numerical diffusion as compared to the finite difference method. Given a desired crystal size distribution, we investigate its reachability from the null initial condition (i.e. without seeding) by controlling the temperature. Some checkable criterion is established to determine if a desired crystal size distribution is reachable. When it is reachable, an admissible temperature control is constructed to steer the states to the desired distribution in finite time. Our construction is developed based on the discretized model and applied for the original model described by partial differential equations. To ensure a desirable distribution to be reached, we add an output feedback control law to correct possible errors given rise to by uncertainty of parameters.