Advanced hybrid-flux approach for output bounds of electro-osmotic flows: adaptive refinement and direct equilibrating strategies

Fluidic flow and species transport in integrated microfluidic devices can readily be simulated with computational fluid dynamics. Nevertheless, the common practice to evaluate the solution accuracy is to decrease the discretization size (i.e., mesh size) until the value of the quantity of interest (termed ‘‘output’’ here-in) does not change within a fixed tolerance. For systems of partial differential equations such as the ones needed to be solved for electro-osmotic flows, this procedure is inappropriate due to the resulting large computation cost when dealing with finer discretizations. Furthermore, in a design environment, when investigating many geometries and flow configurations, the numerical uncertainty in the output may not allow the designer to select the best design. In this paper, we present a numerical technique that is particularly appropriate to provide certainty information for outputs of electro-osmotic microflows. The method uses an a-posteriori error estimation technique termed the bound method to provide fast, inexpensive, and reliable bounds to the ‘‘output’’, therefore, alleviating the need to systematically run different meshes. To demonstrate the usefulness of the bound method, the electro-osmotic flow applied to the cross-intersection in microchannel configuration is analyzed. The bound method presented in this paper is also extend to use an adaptive refinement strategy to sharpen the bounds, the direct equilibrating strategy to calculate the ‘hybrid-flux’ very efficiently, and parallel local computations to speed up the fine h-mesh computations.