Identification and optimization of flow and transport phenomena

**Outline:** Many problems arising in applications, like the validation of flow models or the determination of unobservable field quantities from experimental data, are inverse and ill-posed. This means that reliable solutions can only be found by some sort of regularization. While the principle understanding of linear inverse problems may be considered rather mature, the reliable treatment of nonlinear problems, e.g., many parameter identification problems, is not fully understood. Some problems that attracted significant interest in recent years are the unique continuation from partial observations, the determination of flow parameters, or the imaging of more general transport phenomena. Related problems also arise in shape optimization and optimal control of flow phenomena.

**Goal:** The main aim of this project is to investigate and characterize flow models from indirect measurements. Particular examples are the reconstruction of flow and pressure fields from partial observations of fluid velocities, or the identification of viscosity or turbulence models. The latter amounts to parameter identification problems governed by a fluid flow model, e.g., the incompressible Navier-Stokes equations. Besides analytical questions, like the identifiability of parameters and the stability of solutions, particular emphasis will be put on efficient and stable numerical algorithms for the solution of the governing differential equations and for the resulting inverse problem.

**Challenges:** Parameter identification in partial differential equations typically leads to nonlinear inverse problems. These can be formulated as optimal control problems with pde constraints. An efficient numerical simulation requires the problem adapted solution strategies, efficient solvers for non-linear and linearized pde's, adjoint techniques for computing gradients, and appropriate iterative solvers for the resulting KKT systems. Particular emphasis shall be put on the incorporation of measurement data, obtained by other groups at GSC CE.

Optimal control, Modeling and simulation of coupled multi-physical problems

Template Student

M.Sc./Dipl.-X

Address: | Dolivostraße 15 |

D-64293 Darmstadt | |

Germany | |

Phone: | +49 6151 16 - 23171 |

Fax: | +49 6151 16 - 24404 |

Office: | S4|10-104 |

Email: | |