Numerical methods for coupled normal-fluid and superfluid flows in helium II

Helium II at temperatures below Tλ can be described as a superposition of two interacting fluids. A normal-fluid which has non-zero viscosity, and an inviscid superfluid in which vorticity is confined to quantised vortex filaments. These two fluids are coupled together by the mutual friction force. To model the normal-fluid flow we use the forced Navier-Stokes equation while the superfluid flow is modelled as motion of quantised vortex lines. In this article we describe the numerical methods used for the coupled motion of the two fluids. We also briefly discuss the detailed flow structures observed from the two-dimensional (2-D) and the three-dimensional (3-D) simulations of this problem. (orig.)