A method for numerical simulation of superfluid helium

Superfluid helium Transport phenomena can be described using the two-fluid Landau-Khalatnikov model and the Gorter-Mellink mutual friction. We have continued our previous work devoted to the formulation of a system of equations to describe the heat and mass transport in superfluid helium, and its numerical solution. The main advantage of the approach proposed is that it yields explicitly pressure and temperature as system variables, which can be used to stabilize the numerical solution. In the paper we describe the numerical implementation of the method proposed, and first results on simple test cases that prove the stability and convergence of the procedure.