Integral equations: theory and numerical treatment
Integral equations: theory and numerical treatment
Spectral methods in MATLAB
Shapes and geometries: analysis, differential calculus, and optimization
Shapes and geometries: analysis, differential calculus, and optimization
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Optimal control of the free boundary in a two-phase Stefan problem
Journal of Computational Physics
Mathematical modeling and simulation of aquatic and aerial animal locomotion
Journal of Computational Physics
Adjoint-based optimization of PDEs in moving domains
Journal of Computational Physics
Vortex dynamics in complex domains on a spherical surface
Journal of Computational Physics
A contour dynamics algorithm for axisymmetric flow
Journal of Computational Physics
A variational level set method for the topology optimization of steady-state Navier-Stokes flow
Journal of Computational Physics
Shape optimization towards stability in constrained hydrodynamic systems
Journal of Computational Physics
Simulating the dynamics of flexible bodies and vortex sheets
Journal of Computational Physics
Short Note: On the simulation of nearly inviscid two-dimensional turbulence
Journal of Computational Physics
An inverse model for a free-boundary problem with a contact line: Steady case
Journal of Computational Physics
Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design
Journal of Computational Physics
Shape optimization of peristaltic pumping
Journal of Computational Physics
Regularizing a vortex sheet near a separation point
Journal of Computational Physics
Hi-index | 7.29 |
In this investigation we propose a computational approach for the solution of optimal control problems for vortex systems with compactly supported vorticity. The problem is formulated as a PDE-constrained optimization in which the solutions are found using a gradient-based descent method. Recognizing such Euler flows as free-boundary problems, the proposed approach relies on shape differentiation combined with adjoint analysis to determine cost functional gradients. In explicit tracking of interfaces (vortex boundaries) this method offers an alternative to grid-based techniques, such as the level-set methods, and represents a natural optimization formulation for vortex problems computed using the contour dynamics technique. We develop and validate this approach using the design of 2D equilibrium Euler flows with finite-area vortices as a model problem. It is also discussed how the proposed methodology can be applied to Euler flows featuring other vorticity distributions, such as vortex sheets, and to time-dependent phenomena.