Numerical simulations in astrophysics:Supernovae explosions, magnetorotational model and neutrino emission

Theories of stellar evolution and stellar explosion are based on results of numerical simulations and even qualitative results are not available to get analytically. Supernovae are the last stage in the evolution of massive stars, following the onset of instability, collapse and formation of a neutron star. Formation of a neutron star is accompanied by a huge amount of energy, approximately 20% of the rest mass energy of the star, but almost all this energy is released in the form of weakly interacting and hardly registrated neutrino. About 0.1% of the released neutrino energy would be enough for producing a supernovae explosion, but even transformation of such a small part of the neutrino energy into the kinetic energy of matter meets serious problems. Two variants are investigated for obtaining explosion. The first one is based on development of convective instability, and more effective heating of the outer layers by a neutrino flux. The second model is based on transformation of a rotational energy of a rapidly rotating neutron star with its envelope into the energy of explosion due to action of a magnetic field as a transformation mechanism. Calculations in this model in 1- and 2-dimensions give a stable value of transformation of the rotational energy into the energy of explosion on the level of few percents. This occurrance to be enough for explanation of the energy release in supernova explosion. The last model gives a direct demonstration of nonlinear interaction between hydrodynamical and hydromagnetic systems. At first a field is amplified by differential rotation, then this enhanced field leads to transformation of the rotational energy into the energy of explosion.