Hello !
I’m a Ph.D. student in Mathematics (2024-2027), under the supervision of Carine Lucas, Laurence Girolami, and Olivier Delestre at Institut Denis Poisson and my thesis is funded by the mathematics in interaction research program (PEPR Maths-Vives), ComplexFlow project.
Research interests
During my thesis, I am studying models associated with geophysical flows. Certain natural gravitational flows (pyroclastic flows, lahars, and underwater avalanches), subject to sedimentation processes, are the cause of devastating extreme events that can have serious human and environmental consequences. Predicting their overall behavior (runout, deposit geometry) is a major challenge for the community. I am therefore studying multi-layer Shallow Water models, with a sedimentation process.
\[ \begin{aligned} \partial_t H + \partial_x(H\bar{U}) &= \left( \frac{\phi_{pack}}{\phi_s} - 1 \right) S_{sed}, \\[2mm] \partial_t(H\bar{U}) + \partial_x(H\bar{U}^2) &= \left( \frac{\phi_{pack}}{\phi_s} - 1 \right) S_{sed} \, \bar{U} - g H \, \partial_x(H + h + h_d), \\[2mm] \partial_t h + \partial_x(h\bar{u}) &= S_{slump} - \frac{\phi_{pack}}{\phi_s} S_{sed}, \\[2mm] \partial_t(h\bar{u}) + \partial_x(h\bar{u}^2) &= \left( S_{slump} - \frac{\phi_{pack}}{\phi_s} S_{sed} \right) \bar{u} - \kappa \bar{u} \, \chi(t > t_{ff}) - g h \, \partial_x \left( \frac{\rho_f}{\rho_m} H + h + h_d \right), \\[2mm] \partial_t h_d &= S_{sed} \end{aligned} \] Some simulations of the numerical scheme used and simulations of the model with sedimentation (coming soon) can be found in the Software tab.