(298g) Efficient Numerical Schemes for Population Balance Models

Population balance models (PBMs) describe a wide array of physical, chemical, and biological processes having a distribution over some intrinsic property such as size or age. The ability of PBMs to capture important dynamical processes that impact the distribution such as birth, growth, and attrition have meant that PBMs are commonly used to model systems containing cells, viruses, aggregates, bubbles, and crystals among others. The ubiquity and capability of PBMs motivates generalizable and accurate approaches for their numerical solution. Typically, high-order finite difference or finite volume methods are used, and these methods can be complex and computationally costly. We propose a finite difference scheme based on the classical upwind method at the limit of numerical stability that results in discretization error that is zero for certain classes of PBMs and low enough to be acceptable in other applications. The scheme employs specially constructed meshes and, in some cases, variable transformations. The scheme can be deployed with very low computational cost and high speed, sometimes as low as memory reallocation with no floating-point operations. Case studies considering various classes of PBMs are presented that demonstrate the scheme’s performance in relation to other commonly employed schemes. The low computational cost of this approach enables the explicit incorporation of mechanistic models into dynamic optimization and model predictive control schemes without sacrificing accuracy.