This part is mainly built starting from hillebrandt2000.
The dwarf white one can be described like a plasma completely ionized with a variable degree of degeneration of the electrons. One can regard it as a fluid. The equations which control the phenomenon are then those of the hydrodynamics for the masses, the species, the transport of energy like gravitational acceleration, viscosity, the heat and the diffusion of mass and the nuclear energy production.
The initial conditions (report/ratio C/O, profile of temperature) are obtained starting from the models of dwarf white with spherical symmetry or starting from the equations of Chandrasekhar describing a gas of degenerated electrons at null temperature. By giving the initial conditions, symmetries fix the boundary conditions and one can integrate the equations of the movement in theory directly.
Until the middle of the Nineties, only the studies of model 1D to spherical symmetry were considered. This approach has the principal disadvantage of being able to give an account of a certain number of aspects related with the burn-ups. In particular, lightings out of the heart of dwarf white, of thermodynamic instabilities of the flame or the phenomena of turbulence cannot be taken into account. These phenomena could have significant implications as for the survival of certain models.
Despite everything, the models 1D seem to be today still, the only ones with reasonably being able to marry the hydrodynamic phenomena with a detailed phenomenology of nucleosynthesis and to obtain a global vision of the explosion. In fact, the majority of the models of explosion allowing to make predictions on the spectra and the lightcurves are based on this type of model.