Impacts of Discretization Error, Flow Modeling Error, and Measurement Noise on Inverse Transport-Diffusion-Reaction in a T-Junction

Abstract

By combining a physical model and sensor outputs in an inverse transport-diffusion-reaction strategy, an accurate concentration cartography may be obtained. The paper addresses the influence of discretization errors, flow uncertainties, and measurement noise on the concentration field reconstruction process. We consider a key element of a drinking water network, i.e., a pipe junction, where Reynolds and Peclet numbers are approximately 2000 and 1000, respectively. We show that a 10% error between the reference concentration field and the reconstructed concentration field may be obtained using a coarse discretization. Nevertheless, to keep the error below 10%, a fine concentration discretization is required. We also detail the influence of the flow approximation on the concentration reconstruction process. The flow modeling error obtained when the exact Navier–Stokes flow is approximated by a Stokes flow may lead to a 40% error in the reconstructed concentration. However, if the flow field is obtained from the full set of Navier–Stokes equations, we show that the error may be less than 5%. Then, we observe that the quality of the reconstructed concentration field obtained with the proposed inverse technique is not deteriorated when sensor outputs have a normal distribution noise variance of few percents. Finally, a good engineering practice would be to stop the reconstruction process according to an extended discrepancy principle including modeling and measurement errors. As shown in the paper, the quality of the reconstructed field declines after reaching the threshold of the modeling error.