Abstract
The application of a direct numerical analysis to the superfluid phenomena is attempted. The propagation of a second sound wave and the evolution of a finite amplitude thermal wave into a shock wave are simulated by applying the finite difference scheme to the two-fluid equation for superfluid helium (He II). Typically three types of thermal shock waves, that is to say, a front shock, a back shock and a double shock, are well simulated. The results, however, suggested necessity for introducing the effect of the interaction of a flow field with a tangled mass of quantized vortices to the governing equation in the breakdown state. The effect is taken into account on the basis of the Gorter-Mellink mutual friction formula modified to include an unsteady feature for the simulation of the propagation of a thermal shock, and of a steady heating.
