| Advisor(s) | Alberto Guardone, Dario Isola |
| Expected duration | 6 months (one or two students) |
| Description | The on going research on the development of efficient and accurate schemes continuously sets higher standards, and very promising results have been shown by Flowmesh, the most recent solver developed at DIA. Flowmesh is a finite-volumes solver for the arbitrary Lagrangian-Eulerian (ALE) formulation of the Euler equations that implements a unique strategy that allows to perform adaptive computations without resorting to interpolation. To extend the finite-volume schemes specifically developed for the Euler equations to the viscous case, it is possible to resort to the compatibility relationships with Lagrangian finite-element methods. Indeed the definition of the Laplacian-like term is fairly straightforward in the latter case. However, preliminary results show that such relationships do not hold in the ALE framework, due to the change in shape of the cells. The development of a novel numerical scheme is therefore necessary if the arbitrary Lagrangian-Eulerian formulation is solved with the finite element method. The student is expected to become active member of the Flowmesh developers team and a strong interaction with the rest of the group is mandatory. A significant contribution in terms of the development numerical schemes is expected. Some basic Fortran coding is also required. This thesis is suggested to students that show a specific bias for numerical mathematics. |
| Required tasks | Development of a numerical scheme to solve the ALE formulation of the scalar advection problem over deforming meshes in two and three dimension. Implementation of the ALE-FEM scheme in the Flowmesh program. Comparison of the results with the corresponding finite-volume method. Extension of the scheme to the case of the Euler equations and implementation in Flowmesh. Comparison with the results obtained by the FV scheme for unsteady flows over moving bodies. |
| Tools and languages | Flowmesh, Fortran |
| Prerequisites | Numerical methods for PDE (good), FEM/FV methods (good), Fortran (basic), CFD (good) |
| Outcome | The student is expected to present the work at an international conference and to be co-author of a publications on a reviewed accademic journal |
| Contacts | Please send an email to Alberto Guardone or Dario Isola, see contacts page. |