کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
520189 867700 2009 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
High resolution finite volume scheme for the quantum hydrodynamic equations
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
High resolution finite volume scheme for the quantum hydrodynamic equations
چکیده انگلیسی

The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems.A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher–Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge–Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme.In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10−5 to 10−12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10−4.To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were solved for an Eckart barrier and a downhill ramp barrier, respectively. The results were compared to the solution of the Schrödinger equation, using the same potentials, which was obtained using by a finite difference method. Finally, the new approach was applied to simulate a quantum nanojet system and offer more intact theory in quantum computational fluid dynamics.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 228, Issue 5, 20 March 2009, Pages 1713–1732
نویسندگان
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