Dispersion–current adjoint functions for monitoring accidental sources in 3D transport equations

Abstract

ABSTRACT The paper deals with the identification of multiple unknown time-dependent point sources occurring in 3D dispersion–advection–reaction equations. Based on the developed appropriate adjoint functions, we establish a constructive identifiability result depending on the flow nature that yields guidelines leading to a quasi-direct detection–identification method. In practice, assuming to be available within a monitored domain some interfaces subdividing it into suspected sections, the developed method goes throughout the entire domain to detect the presence of all active sources. If an activity is detected within a suspected section, the method identifies the total amount discharged in this section and determines whether it is done by a single or multiple unknown occurring sources. Moreover, it localizes the sought position of a detected source as the unique root of a dispersion–current vector function defined from the developed adjoint functions. Application to different types of flow and some numerical experiments on the surface water pollution are presented.