Generating Scalable and Modular Macromodels for Microchannels Using the Galerkin-Based Technique

In this paper, we present a methodology of generating nonlinear microfluidic macromodels for system-level simulations of 3-D microchannels using the Galerkin-based technique. Each generated macromodel consists of a low-order model and a few basis functions. For generating the basis functions, the ensembles of snapshots of fluidic field distributions are calculated by a finite-element-method or finite-volume-method solver, and then, the proper orthogonal decomposition is employed to extract the basis functions from the ensembles. For creating the low-order model, the Galerkin condition is used to formulate a set of simple ordinary differential equations. Compared with the full-meshed simulations, the generated macromodels not only provide accurate results (i.e., about 1% error) but also give computational speedups of at least three orders of magnitude. Also, the scaling and reusability of the generated macromodels are described and discussed. Furthermore, the macromodels of complicated channels can also be created by assembling the macromodels of other simple channels. The errors between the results by the assembled macromodels and the results by the full-meshed models are less than 2%.