|Résumé :||In this doctoral work, we adress various problems arising when dealing with multi-physical simulations using a segregated (non-monolithic) approach. We concentrate on a few specific problems and focus on the solution of aeroelastic
flutter for linear elastic structures in compressible fl
ows, conjugate heat transfer for re-entry vehicles including thermo-chemical reactions and finally, industrial electro-chemical plating processes which often include
stiff source terms. These problems are often solved using specifically developed
solvers, but these cannot easily be reused for different purposes. We have therefore considered the development of a
flexible and reusable software platform for the simulation of multi-physics problems. We have based this
development on the COOLFluiD framework developed at the von Karman Institute in collaboration with a group of partner institutions.
For the solution of fl
ow problems involving compressible
flows, we have used the Finite Volume method and we have focused on the application of the method to moving and deforming computational domains using the Arbitrary Lagrangian Eulerian formulation. Validation on a series of testcases (including turbulent flows) is shown. In parallel, novel time integration
methods have been derived from two popular time discretization methods.
They allow to reduce the computational effort needed for unsteady fl
Good numerical properties have been obtained for both methods.
For the computations on deforming domains, a series of mesh deformation techniques are described and compared. In particular, the effect of the stiffness definition is analyzed for the Solid material analogy technique. Using
the techniques developed, large movements can be obtained while preserving a good mesh quality. In order to account for very large movements for which mesh deformation techniques lead to badly behaved meshes, remeshing is also considered.
We also focus on the numerical discretization of a class of physical models that are often associated with
ows in coupled problems. For the elliptic problems considered here (elasticity, heat conduction and electrochemical
potential problems), the implementation of a Finite Element solver is presented. Standard techniques are described and applied for a variety of problems, both steady and unsteady.
Finally, we discuss the coupling of the
fluid flow solver with the finite element solver for a series of applications. We concentrate only on loosely and strongly coupled algorithms and the issues associated with their use and implementation. The treatment of non-conformal meshes at the interface between two coupled computational domains is discussed and the problem
of the conservation of global quantities is analyzed. The software development of a
flexible multi-physics framework is also detailed. Then, several coupling algorithms are described and assessed for testcases in aeroelasticity and conjugate heat transfer showing the integration of the
fluid and solid solvers within a multi-physics framework. A novel strongly coupled algorithm, based on a Jacobian-Free Newton-Krylov method is also presented and applied to stiff coupled electrochemical potential problems.