მათემატიკის დეპარტამენტის სამეცნიერო სემინარის სხდომა

Core-collapse supernovae herald the spectacular death of massive stars by an energetic explosion. The complexity of the arising fluid instabilities in multiple dimensions can only be tackled by numerical means. After a brief introduction of the problem, we will focus on the numerical modeling. The physical system can be described by the equations of radiation-magnetohydrodynamics which form a non-linear system of conservation laws with source terms. We will outline the solution methods of this non-linear set of PDEs with the focus on our contribution to the algorithms. In the course of the simulation, a highly compact proto-neutron star forms. On the explosion time scale of a few hundreds of milliseconds, this object evolves approximately in hydrostatic equilibrium and a numerical scheme should be able to hold this near hydrostatic equilibrium and, at the same time, accurately model perturbations on top of it. To achieve this, we developed a well-balanced method for the treatment of balance laws near stationary state that preserves a discrete form of the hydrostatic equilibrium.