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Efficient simulation of semilinear populations models for age-structured bio reactors

In this contribution we introduce an efficient simulation scheme for a class of hyperbolic dynamic systems, which model the age-structured evolution of a microorganism population in a bio reactor. Due to the non-local boundary condition and the semilinear transient behavior, standard methods like finite-differences do not lead to satisfactory results, even at high approximation orders. This gives rise to advanced simulation schemes: The presented algorithm utilizes the framework of weighted residuals and preserves crucial properties of the PDE system. For instance, we incorporate the steady state solution of the PDE system and guarantee a vanishing steady state approximation error — independent of the order.