Reconstruction of obstacles in a Stokes flow as a shape-from-moments problem

TL;DR

This paper transforms the inverse problem of identifying obstacles in a Stokes flow into a shape-from-moments problem, enabling improved reconstruction methods validated by numerical tests.

Contribution

It introduces a novel approach converting obstacle reconstruction in Stokes flow into a shape-from-moments problem, enhancing existing methods.

Findings

Numerical tests show significant improvements over previous methods.

The shape-from-moments formulation is effective for obstacle reconstruction.

The approach provides a new framework for inverse problems in fluid dynamics.

Abstract

We address the classical inverse problem of recovering the position and shape of obstacles immersed in a planar Stokes flow using boundary measurements. We prove that this problem can be transformed into a shape-from-moments problem to which ad hoc reconstruction methods can be applied. The effectiveness of this approach is confirmed by numerical tests that show significant improvements over those available in the literature to date.