Identification of a boundary obstacle in a Stokes fluid with Dirichlet–Navier boundary conditions: External measurements

Abstract

The problem of identifying an obstruction within a fluid duct has several applications, one of which is in medicine, where the presence of stenosis in coronary vessels poses a life-threatening disease. In this paper, we formulate a continuous setting and study from a numerical perspective the inverse problem of identifying an obstruction contained in a 2D duct where a Stokes flow hits the boundary (subject to Dirichlet and Navier-slip boundary conditions), generating an acoustic wave. To be precise, using acoustic wave measurements at certain points on the exterior of the duct, we can identify the location, extent, and height of the obstruction. Thus, our framework offers an external approach to solving this inverse-obstacle problem. Synthetic examples are used to verify the effectiveness of the proposed numerical formulation.