Quantum Fluid Dynamics and Quantum Computational Fluid Dynamics

The aim of this work is to present physical principles and numerical simulation on the applications of quantum fluid mechanics (QFM). Taking advantage of the ontological explanation of quantum mechanics (QM), the examination of the behaviors of atoms, molecules and quantum systems can be used by the method. The quantum fluids satisfy the laws of conservation that derived from the theoretical framework of quantum mechanics. It can be described by probability and also by alternative mathematical representation. The fluid descriptions of selected condition such as quantum systems, quantum slabs, wires and quantum dots, particle emitter, and hydrogen atom are compared with the descriptions of wave formalism of Schrodinger to elucidate non-linear quantum physical phenomena, which have not been treated by the quantum mechanics. Basic fluid dynamic W behaviors of various configurations at non-steady state are examined and the dispersion relations at different degrees of quantum effects are studied. Here a finite volume scheme is developed to solve the quantum hydrodynamic equations and the accuracy and stability is improved significantly. The quantum fluid dynamics (QFD) equation is numerically implemented within the Eularian approach. A third-order modified Osher-Chakravarthy (MOC) upwind finite-volume scheme was constructed 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 was applied to perform the time integration to enhance the convergence of the proposed scheme. The potential applications of quantum fluid dynamics and quantum computational fluid dynamics in the nanoscience area are discussed in this paper.