Adjoint-Consistent Formulations of Slip Models for Coupled Electroosmotic Flow Systems
byV.V. Garg, S. Prudhomme, K.G. Van Der Zee, G.F. Carey
V.V. Garg, S. Prudhomme, K.G. van der Zee, and G.F. Carey, Adjoint-Consistent Formulations of Slip Models for Coupled Electroosmotic Flow Systems, Advanced Modeling and Simulation in Engineering Sciences 2014 2:15.
The objective of this paper is to construct adjoint-consistent formulations of the Helmholtz ‘slip’ model used for the simulation of electroosmotic flows. The motivation is to develop adjoint-based, adaptive mesh refinement and parameter sensitivity analysis tools for microfluidic problems. A direct formulation of the ‘slip’ model leads to an ill-posed adjoint problem and may yield suboptimal convergence rates. A modified formulation of the coupled ‘slip’ model is proposed, for which the corresponding adjoint problem is shown to be well-posed and provides adjoint solutions that can in turn be employed for mesh refinement and sensitivity analysis. Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional test problems.