This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which ca...This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.展开更多
This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT prob...This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.展开更多
This paper presents a practical guide for use of the ScalIT software package to perform highly accurate bound rovibrational spectroscopy calculations for triatomic molecules. At its core, ScalIT serves as a massively ...This paper presents a practical guide for use of the ScalIT software package to perform highly accurate bound rovibrational spectroscopy calculations for triatomic molecules. At its core, ScalIT serves as a massively scalable iterative sparse matrix solver, while assisting modules serve to create rovibrational Hamiltonian matrices, and analyze computed energy levels (eigenvalues) and wavefunctions (eigenvectors). Some of the methods incorporated into the package include: phase space optimized discrete variable representation, preconditioned inexact spectral transform, and optimal separable basis preconditioning. ScalIT has previously been implemented successfully for a wide range of chemical applications, allowing even the most state-of-the-art calculations to be computed with relative ease, across a large number of computational cores, in a short amount of time.展开更多
In order to establish a well-balanced scheme, 2D shallow water equations were transformed and solved by using the Finite Volume Method （FVM） with unstructured mesh. The numerical flux from the interface between cell...In order to establish a well-balanced scheme, 2D shallow water equations were transformed and solved by using the Finite Volume Method （FVM） with unstructured mesh. The numerical flux from the interface between cells was computed with an exact Riemann solver, and the improved dry Riemann solver was applied to deal with the wet/dry problems. The model was verified through computing some typical examples and the tidal bore on the Qiantang River. The results show that the scheme is robust and accurate, and could be applied extensively to engineering problems.展开更多
The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equil...The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.展开更多
We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation(MSBTE)for the two dimensional(2D)electron gas in double gate metal oxide semiconductor field effect transistors(MOSFE...We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation(MSBTE)for the two dimensional(2D)electron gas in double gate metal oxide semiconductor field effect transistors(MOSFETs)with flared out source/drain contacts.A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is solved.We propose a second order finite volume method based on the positive and flux conservative(PFC)method to discretize the Boltzmann transport equations(BTEs).The transport part of the BTEs is split into two problems.One is a 1D transport problem in the position space,and the other is a 2D transport problem in the wavevector space.In order to reduce the splitting error,the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D problems.The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is investigated.Comparison of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.展开更多
A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow...A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.展开更多
基金Project supported by the National Natural Science Foundation of China(U1630249,11971071,11971069,11871113)the Science Challenge Project(JCKY2016212A502)the Foundation of Laboratory of Computation Physics.
文摘This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.
基金Scientific Research Project for Introduced Talents of Guizhou University of Finance and Economics(No.2021YJ007)National Natural Science Foundation of China(Grant Nos.61862051,61762019,62241206)+2 种基金Top-notch Talent Program of Guizhou Province(No.KY[2018]080)Science and Technology Foundation of Guizhou Province(No.20191299)foundation of Qiannan Normal University for Nationalities(Nos.QNSYRC201715,QNSY2018JS013).
文摘This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.
文摘This paper presents a practical guide for use of the ScalIT software package to perform highly accurate bound rovibrational spectroscopy calculations for triatomic molecules. At its core, ScalIT serves as a massively scalable iterative sparse matrix solver, while assisting modules serve to create rovibrational Hamiltonian matrices, and analyze computed energy levels (eigenvalues) and wavefunctions (eigenvectors). Some of the methods incorporated into the package include: phase space optimized discrete variable representation, preconditioned inexact spectral transform, and optimal separable basis preconditioning. ScalIT has previously been implemented successfully for a wide range of chemical applications, allowing even the most state-of-the-art calculations to be computed with relative ease, across a large number of computational cores, in a short amount of time.
基金Project supported by the Natural Science Foundation of Zhejiang Province (Grant No: M403054).
文摘In order to establish a well-balanced scheme, 2D shallow water equations were transformed and solved by using the Finite Volume Method （FVM） with unstructured mesh. The numerical flux from the interface between cells was computed with an exact Riemann solver, and the improved dry Riemann solver was applied to deal with the wet/dry problems. The model was verified through computing some typical examples and the tidal bore on the Qiantang River. The results show that the scheme is robust and accurate, and could be applied extensively to engineering problems.
基金supported by the National Basic Research Program of China(Grant No.2013CB430403)the Public Science and Technology Research Funds Projects of Ocean(Grant No.201205023)+3 种基金the Program for Liaoning Excellent Talents in University(Grant No.LJQ2013077)the Science and Technology Foundation of Dalian City(Grant No.2013J21DW009)the Special Funds for Postdoctoral Innovative Projects of Liaoning Province(Grant No.2011921018)the Special Funds for Talent Projects of Dalian Ocean University(Grant No.SYYJ2011004)
文摘The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.
基金supported by the NKBRP(Grants 2006CB302705,2005CB321704)the NSFC(Grants 10701005,11011130029)sponsored by SRF for ROCS,SEM.
文摘We propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation(MSBTE)for the two dimensional(2D)electron gas in double gate metal oxide semiconductor field effect transistors(MOSFETs)with flared out source/drain contacts.A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is solved.We propose a second order finite volume method based on the positive and flux conservative(PFC)method to discretize the Boltzmann transport equations(BTEs).The transport part of the BTEs is split into two problems.One is a 1D transport problem in the position space,and the other is a 2D transport problem in the wavevector space.In order to reduce the splitting error,the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D problems.The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is investigated.Comparison of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.
文摘A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.
