Open AccessA distributed resistance inverse method for flow obstacle identification from internal velocity measurements
Author(s) -
Jorge Aguayo,
C Bertoglio,
Axel Osses
Publication year - 2021
Publication title -
inverse problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.003
H-Index - 119
eISSN - 1361-6420
pISSN - 0266-5611
DOI - 10.1088/1361-6420/abced8
Subject(s) - inverse problem , mathematics , obstacle , differentiable function , flow (mathematics) , inverse , mathematical analysis , boundary value problem , domain (mathematical analysis) , boundary (topology) , compressibility , uniqueness , vector field , incompressible flow , navier–stokes equations , geometry , mechanics , physics , political science , law
We present a penalization parameter method for obstacle identification in an incompressible fluid flow for a modified version of the Oseen equations. The proposed method consists in adding a high resistance potential to the system such that some subset of its boundary support represents the obstacle. This allows to work in a fixed domain and highly simplify the solution of the inverse problem via some suitable cost functional. Existence of minimizers and first and second order optimality conditions are derived through the differentiability of the solutions of the Oseen equation with respect to the potential. Finally, several numerical experiments using Navier–Stokes flow illustrate the applicability of the method, for the localization of a bi-dimensional cardiac valve from MRI and ultrasound flow type imaging data.