Polydispersed particles are frequently described in terms of a property distribution whose evolution is governed by the population balance equation (PBE). In the present article, we develop a numerical solution scheme for the univariate, spatially inhomogeneous PBE that allows for the economical resolution of the particle size distribution at a moderate accuracy and is robust with respect to growth-dominated applications. The method combines the notion of characteristic curves in particle size space with a constrained Galerkin projection and is informed by a training step for the identification of representative shape functions. This step is based on the proper orthogonal decomposition (POD) of snapshot matrices containing adaptive grid solutions of the PBE obtained in simplified flow configurations. In order to assess the viability, accuracy and convergence properties of the combined PBE-POD approach, we analyze the pure growth and dispersion in a laminar plane jet of a polysized particle population.

多分散粒子经常用属性分布来描述，其演化由种群平衡方程 (PBE) 控制。在本文中，我们为单变量、空间非均匀 PBE 开发了一个数值解方案，该方案允许以中等精度经济地解析粒度分布，并且对于生长主导的应用是稳健的。该方法将粒度空间中的特征曲线概念与受约束的伽辽金投影相结合，并通过用于识别代表性形状函数的训练步骤提供信息。此步骤基于包含在简化流配置中获得的 PBE 自适应网格解决方案的快照矩阵的正确正交分解 (POD)。为了评估可行性，