TY - JOUR

T1 - A method for the three-dimensional numerical simulation of superfluid helium

AU - Bottura, L.

AU - Darve, C.

AU - Patankar, N. A.

AU - Van Sciver, W.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - Transport phenomena in superfluid helium can be described using the two-fluid Landau-Khalatnikov model and the Gorter-Mellink mutual friction. Here we discuss a mathematical formulation of the two-fluid model that uses macroscopic conservation balances of mass, momentum and energy of each species, and assumes local thermodynamic equilibrium. A particularity of this model is that it describes the state of He II as well as that of each of the two-fluid components in terms of pressure p and temperature T, which is convenient for stable numerical solution. The equations of the model form a system of partial differential equations (PDE) that can be written in matrix form for convenience. On this base, a three-dimensional numerical model using a complete and consistent, while still practical, system of PDEs was developed. In the form described, the PDE can be solved using three-dimensional Lagrangian finite element in space supplemented by a Beam-Warming time-marching algorithm. Once validated, this solver will allow to simulate He II thermal counter-flow applied to arbitrary geometry.

AB - Transport phenomena in superfluid helium can be described using the two-fluid Landau-Khalatnikov model and the Gorter-Mellink mutual friction. Here we discuss a mathematical formulation of the two-fluid model that uses macroscopic conservation balances of mass, momentum and energy of each species, and assumes local thermodynamic equilibrium. A particularity of this model is that it describes the state of He II as well as that of each of the two-fluid components in terms of pressure p and temperature T, which is convenient for stable numerical solution. The equations of the model form a system of partial differential equations (PDE) that can be written in matrix form for convenience. On this base, a three-dimensional numerical model using a complete and consistent, while still practical, system of PDEs was developed. In the form described, the PDE can be solved using three-dimensional Lagrangian finite element in space supplemented by a Beam-Warming time-marching algorithm. Once validated, this solver will allow to simulate He II thermal counter-flow applied to arbitrary geometry.

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U2 - 10.1088/1742-6596/150/1/012008

DO - 10.1088/1742-6596/150/1/012008

M3 - Article

AN - SCOPUS:65649132297

VL - 150

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

M1 - 012008

ER -