Managing false diffusion during second-order upwind simulations of liquid micromixing

Liquid mixing is an important component of many microfluidic concepts and devices, and computational fluid dynamics (CFD) is playing a key role in their development and optimization. Because liquid mass diffusivities can be quite small, CFD simulation of liquid micromixing can over predict the degree of mixing unless numerical (or false) diffusion is properly controlled. Unfortunately, the false diffusion behavior of higher-order finite volume schemes, which are often used for such simulations, is not well understood, especially on unstructured meshes. To examine and quantify the amount of false diffusion associated with the often recommended and versatile second-order upwind method, a series of numerical simulations was conducted using a standardized two-dimensional test problem on both structured and unstructured meshes. This enabled quantification of an ` effective' false diffusion coefficient (D-false) for the method as a function of mesh spacing. Based on the results of these simulations, expressions were developed for estimating the spacing required to reduce D-false to some desired (low) level. These expressions, together with additional insights from the standardized test problem and findings from other researchers, were then incorporated into a procedure for managing false diffusion when simulating steady, liquid micromixing. To demonstrate its utility, the procedure was applied to simulate flow and mixing within a representative micromixer geometry using both unstructured (triangular) and structured meshes. Copyright (C) 2016 John Wiley & Sons, Ltd.