A. Jüngel, J. Milisic:
"Full compressible Navier-Stokes equations for quantum fluids: derivation and numerical solution";
Kinetic and Related Models, 4 (2011), 3; S. 785 - 807.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
Navier-Stokes equations for compressible quantum
uids, including
the energy equation, are derived from a collisional Wigner equation, using
the quantum entropy maximization method of Degond and Ringhofer. The viscous
corrections are obtained from a Chapman-Enskog expansion around the
quantum equilibrium distribution and correspond to the classical viscous stress
tensor with particular viscosity coe cients depending on the particle density
and temperature. The energy and entropy dissipations are computed and discussed.
Numerical simulations of a one-dimensional tunneling diode show the
stabilizing e ect of the viscous correction and the impact of the relaxation
terms on the current-voltage charcteristics.

Quantum Navier-Stokes equations; Chapman-Enskog expansion; semiconductor devices

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