The multi-mode approximation is presented to compute the interior wave function of Schr¨odinger equation.This idea is necessary to handle the multi-barrier and high dimensional resonant tunneling problems where m...The multi-mode approximation is presented to compute the interior wave function of Schr¨odinger equation.This idea is necessary to handle the multi-barrier and high dimensional resonant tunneling problems where multiple eigenvalues are considered.The accuracy and efficiency of this algorithm is demonstrated via several numerical examples.展开更多
An accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three stati...An accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics.The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term.The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of the discretized velocity distribution function in physical space and time.The method is developed for two space dimensions and implemented on gas particles that obey the Maxwell-Boltzmann,Bose-Einstein and Fermi-Dirac statistics.Computational examples in one-and two-dimensional initial value problems of rarefied gas flows are presented and the results indicating good resolution of the main flow features can be achieved.Flows of wide range of relaxation times and Knudsen numbers covering different flow regimes are computed to validate the robustness of the method.The recovery of quantum statistics to the classical limit is also tested for small fugacity values.展开更多
基金supported by the Conseil regional Midi Pyrenees(http://www.midipyrenees.fr/)entitled"Methodes Numeriques Multi-echelles pour le transport quantique"and by the ANR Project No.BLAN07-2212988 entitled"QUATRAIN")support from NSFC Projects 11071139 and NSFC Projects 10971115.
文摘The multi-mode approximation is presented to compute the interior wave function of Schr¨odinger equation.This idea is necessary to handle the multi-barrier and high dimensional resonant tunneling problems where multiple eigenvalues are considered.The accuracy and efficiency of this algorithm is demonstrated via several numerical examples.
基金TAIWAN through grants NSC-99-2922-I-606-002CQSE subproject No.599R-80873+1 种基金the support by project No.599R-80873by National Nature Science Foundation of China under grant No.91016027.
文摘An accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics.The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term.The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of the discretized velocity distribution function in physical space and time.The method is developed for two space dimensions and implemented on gas particles that obey the Maxwell-Boltzmann,Bose-Einstein and Fermi-Dirac statistics.Computational examples in one-and two-dimensional initial value problems of rarefied gas flows are presented and the results indicating good resolution of the main flow features can be achieved.Flows of wide range of relaxation times and Knudsen numbers covering different flow regimes are computed to validate the robustness of the method.The recovery of quantum statistics to the classical limit is also tested for small fugacity values.
