Numerical Computation of Thermal Shock Wave in HE II

Abstract

Application of the numerical computation is attempted to the two- fluid equations for superfluid helium. The propagation of thermal shock waves is numerically simulated by applying a finite difference method, MacCormack’s forward-predictor backward-corrector method. The thermodynamic quantities are computed as functions of temperature and pressure with the aid of the interpolation of data presented by Faynard. The numerical result shows that for moderately strong shock waves the relative velocity between the normal and super components amounts to several m/s, and the superfluid breakdown phenomena should be considered. The mutual- friction term is introduced to the two-fluid equation system, for which the time for the development of vortices must be considered through the modified Gorter-Mellink coefficient A = A(T,t). The computational results qualitatively agree with experimental data.