| Abstract: |
| In quantum flows, like liquid helium II at intermediate temperatures between zero and 2.17 K, a normal fluid and a superfluid coexist with independent velocity fields. The most advanced existing models for such systems use the Navier-Stokes equations for the normal fluid and a simplified description of the superfluid, based on the dynamics of quantized vortex filaments, with ad hoc reconnection rules. There was a single attempt [1] to couple Navier-Stokes and Gross-Pitaevskii equations in a global model intended to describe the compressible two-fluid liquid helium II.
We present in this contribution a new numerical model to couple a Navier-Stokes incompressible fluid with a Gross-Pitaevskii superfluid [2]. A numerical algorithm based on pseudo-spectral Fourier methods is presented for solving the coupled system of equations. The new numerical system is validated against well-known benchmarks for the evolution in a normal fluid of different types or arrangements of quantized vortices (vortex crystal, vortex dipole and vortex rings).
[1] C. Coste, Nonlinear Schrodinger equation and superfluid hydrodynamics, The European Physical Journal B - Condensed Matter and Complex Systems, VOL. 1, P. 245--253, 1998.
[2] M. Brachet, G. Sadaka, Z. Zhang, V. Kalt and I. Danaila, Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows, J. Computational Physics, 488, p. 112193(1-17), 2023. |
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