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June 2007 Physical and numerical viscosity for quantum hydrodynamics
Ansgar Jüngel, Jospa Pina Milišić
Commun. Math. Sci. 5(2): 447-471 (June 2007).


Viscous stabilizations of the quantum hydrodynamic equations are studied. The quantum hydrodynamic model consists of the conservation laws for the particle density, momen- tum, and energy density, including quantum corrections from the Bohm potential. Two different stabilizations are analyzed. First, viscous terms are derived using a Fokker-Planck collision operator in the Wigner equation. The existence of solutions (with strictly positive particle density) to the isothermal, stationary, one-dimensional viscous model for general data and nonhomogeneous boundary conditions is shown. The estimates depend on the viscosity and do not allow to perform the inviscid limit. Second, the numerical viscosity of the second upwind finite-difference discretization of the inviscid quantum hydrodynamic model is computed. Finally, numerical simulations using the non-isothermal, stationary, one-dimensional model of a resonant tunnelling diode show the influence of the viscosity on the solution.


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Ansgar Jüngel. Jospa Pina Milišić. "Physical and numerical viscosity for quantum hydrodynamics." Commun. Math. Sci. 5 (2) 447 - 471, June 2007.


Published: June 2007
First available in Project Euclid: 9 July 2007

zbMATH: 1130.76088
MathSciNet: MR2334851

Primary: 35J40 , 65N05 , 76Y05

Keywords: existence of stationary solutions , numerical dispersion , numerical viscosity , quantum hydrodynamics , resonant tunnelling diode , semiconductors , viscous quantum hydrodynamics

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 2 • June 2007
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