An optimal control method for time-dependent fluid-structure interaction problems

Abstract

In this article, we derive an adjoint fluid-structure interaction (FSI) system in an arbitrary Lagrangian-Eulerian (ALE) framework, based upon a one-field finite element method. A key feature of this approach is that the interface condition is automatically satisfied and the problem size is reduced since we only solve for one velocity field for both the primary and adjoint system. A velocity (and/or displacement)-matching optimisation problem is considered by controlling a distributed force. The optimisation problem is solved using a gradient descent method, and a stabilised Barzilai-Borwein method is adopted to accelerate the convergence, which does not need additional evaluations of the objective functional. The proposed control method is validated and assessed against a series of static and dynamic benchmark FSI problems, before being applied successfully to solve a highly challenging FSI control problem.

A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

“…We first validate the scheme using a flow control problem which is widely studied in literature. The second numerical test is a benchmark FSI problem whose controllability is studied by an ALE formulation in [80], and we will show that the proposed two-mesh method will achieve the same goal of reduction of the objective. Our third numerical experiment involves controlling a large-deformed solid; this problem is widely studied as a forward FSI problem in literature, which however has not been considered as an inverse control problem up to now.…”

“…In this test, we consider a benchmark FSI problem of an oscillating leaflet attached to a cylinder [23,80,81], and our objective is to minimise the solid deflection through an activation force on the solid leaflet. The computational domain is a rectangle (L × H) with a cut hole of radius r and center (c, c) as shown in Figure 6.…”

A monolithic one-velocity-field optimal control formulation for fluid–structure interaction problems with large solid deformation

“…We first validate the scheme using a flow control problem which is widely studied in literature. The second numerical test is a benchmark FSI problem whose controllability is studied by an ALE formulation in [80], and we will show that the proposed two-mesh method can reduce the objective as effectively as the ALE method. Our third numerical experiment involves controlling a large-deformed solid; this problem is widely studied as a forward FSI problem in literature, which however has not been considered as an inverse control problem up to now.…”

A monolithic optimal control method for displacement tracking of Cosserat rod with application to reconstruction of C. elegans locomotion

“…Optimal control theory has a wide range of applications from classical control of solid structures [45,60,64,77,84] to optimal flow control [33,43,44,61,65] including recent control formulation for fluid-structure interaction systems [13,14,62,[80][81][82]. The objective can be a desired deformed configuration of an elastic solid controlled by a set of load parameters [45], drag force reduction of a flow system by shape optimisation [33,61,65] or active turbulence control at the boundary layer [15,22,46,50,59,61]; it could also be velocity tracking by controlling a body force [3,36,38,40,43,44,55,57,58,66] or boundary force [3,4,26,28,37,38,41]; the objective may also be reducing vorticity [1,3,66] or matching a turbulence kinetic energy …”