Abstract
Multivariable cell population balance models are commonly used to explain complicated biological phenomena associated with product formation and cell growth in microbial populations. Such models typically consist of a partial integrodifferential equation for describing cell growth and an ordinary integrodifferential equation for representing substrate consumption. Due to their mathematical complexities, the numerical solutions of such models are hard tasks for numerical schemes. In this article, semidiscrete high resolution flux-limiting finite volume schemes are applied to solve single-variate and bivariate cell population balance models. The schemes have the abilities to achieve narrow peaks and resolve sharp discontinuities in the solutions on coarse meshes. These schemes are cheaper due to their short and reliable computational coding for complex problems. Several case studies are carried out. The numerical results of the schemes are compared with each other in terms of CPU time and accuracy. After consideration of different growth rate functions and incorporating equal and unequal partitioning, the suggested schemes were found to be more reliable and effective.
Published Version
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