Theses
last modified
Apr 20, 2021 12:13 PM
Title: Structure preserving schemes for 3D magnetohydrodynamics (MHD)
Description: development of high order numerical methods for the discretization of the ideal MHD equations on structured Cartesian meshes. Particular care will be devoted to the construction of a structure preserving method that is able to maintain at the discrete level the involution on the divergence of the magnetic field exhibited by the governing equations at the continuous level.
Professor: Walter Boscheri
Title: Lagrangian finite volume schemes for solid mechanics on unstructured meshes
Description: development of novel cell-centered Lagrangian methods for the solution of the hyperelasticity equations on moving domains discretized with triangles and tetrahedra. Plasticity effects will be also considered by suitable source terms which might become stiff. Therefore, locally implicit schemes must be designed to ensure numerical stability with reasonably large time steps.
Professor: Walter Boscheri
Title: Implicit-explicit schemes for low Mach flows free surface flows on staggered Voronoi meshes
Description: development of a numerical method for the solution of the free surface equations on general polygonal meshes in xy and z-layer in the vertical direction. To enable the simulation at very low Mach number, which typically occurs in environmental flows, an implicit discretization of the pressure terms will be employed, while the nonlinear convective contributions will be explicitly solved at the aid of a conservative finite volume scheme. Discontinuous Galerkin discretizations will be used for the implicit part of the system, that implies the resolution of an elliptic wave equation on the pressure.
Professor: Walter Boscheri
