Physical and numerical viscosity for quantum hydrodynamics
Physical and numerical viscosity for quantum hydrodynamics
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DOI：
10.4310/cms.2007.v5.n2.a11
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发表时间：
2007
影响因子：
1
通讯作者：
A. Jüngel;J. Milǐsić
中科院分区：
文献类型：
--
作者：
A. Jüngel;J. Milǐsić
研究了量子流体动力学方程的粘性稳定化。量子流体力学模型由粒子密度、动量和能量密度的守恒定律组成，包括来自玻姆势的量子修正。两种不同的稳定化进行了分析。首先，粘性条款推导出使用Fokker-Planck碰撞算子的维格纳方程。解决方案的存在性（严格正粒子密度）的等温，固定，一维粘性模型的一般数据和非齐次边界条件。估计值取决于粘度，不允许执行无粘极限。其次，计算了无粘量子流体动力学模型的二阶迎风有限差分离散的数值粘性。最后，数值模拟使用的非等温的，固定的，一维模型的共振隧穿二极管显示的粘度上的解决方案的影响。
Viscous stabilizations of the quantum hydrodynamic equations are studied. The quantum hydrodynamic model consists of the conservation laws for the particle density, momentum, 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 tunneling diode show the influence of the viscosity on the solution.