Feasibility Analysis of a POD-Based Reduced Order Model with Application in Eulerian-Lagrangian Simulations

Computational fluid dynamics coupled with the discrete element method (CFD-DEM) is widely employed for simulating multiphase flows involving particles, but the heavy computational cost is a major concern. Reduced order models (ROMs) based on proper orthogonal decomposition (POD) offer new potential to greatly reduce the computational cost. This study aims to investigate the feasibility of POD-based ROMs for Eulerian-Lagrangian simulations, considering the few studies in this field. For feasibility analysis, whether the dominant POD modes are essentially similar between the training and testing data sets is a crucial condition. If this condition is not perfectly met, an inconsistent training problem easily takes place, resulting in a so-called consistency error. This error could deteriorate the predictability of a POD-based ROM. Based on a theoretical analysis of consistency error, the most accurate solution that POD-based ROMs can produce is obtained. Furthermore, not only a new common POD-mode number between the training and testing data sets but also a novel predictability ratio are proposed for general feasibility analysis. The simulations of fluidized and spouted beds are taken as examples to show the application of the feasibility analysis. It is found that the POD-based ROM shows poor and excellent predictability for Lagrangian and Eulerian variables, respectively. Thus, it is suggested to map Lagrangian variables in DEM simulations on fixed Eulerian meshes to improve the predictability of the solid particle behavior in the POD-based ROM.