In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids....In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.展开更多
In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal ste...In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.展开更多
In the present work, we numerically study the laminar natural convection of a nanofluid confined in a square cavity. The vertical walls are assumed to be insulated, non-conducting, and impermeable to mass transfer. Th...In the present work, we numerically study the laminar natural convection of a nanofluid confined in a square cavity. The vertical walls are assumed to be insulated, non-conducting, and impermeable to mass transfer. The horizontal walls are differentially heated, and the low is maintained at hot condition (sinusoidal) when the high one is cold. The objective of this work is to develop a new height accurate method for solving heat transfer equations. The new method is a Fourth Order Compact (F.O.C). This work aims to show the interest of the method and understand the effect of the presence of nanofluids in closed square systems on the natural convection mechanism. The numerical simulations are performed for Prandtl number ( ), the Rayleigh numbers varying between and for different volume fractions varies between 0% and 10% for the nanofluid (water + Cu).展开更多
Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundar...Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.展开更多
The internal friction behavior of Al green power compact duxing the sintering process was studied as a function of temperature. The internal friction measurements were performed from room temperature to 600 °C. T...The internal friction behavior of Al green power compact duxing the sintering process was studied as a function of temperature. The internal friction measurements were performed from room temperature to 600 °C. Two typical internal friction peaks were detected corresponding to heating and cooling processes, respectively. The heating peak corresponds to a recrystallization process of deformed Al particles, which is influenced by many extrinsic parameters, such as measuring frequency, strain amplitude, heating rate, power particle size and compacting pressure. However, the intrinsic nature of the peak is originated from the micro-sliding of the weak-bonding interfaces between Al particles and increased dislocation density induced in compressing. The cooling peak with the activation energy of (1.64±0.06) eV is associated with the grain boundary relaxation, which can be interpreted as the viscous sliding of grain boundaries. The similar phenomena are also found in the Mg green powder compact.展开更多
To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams(RCCDs),mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring art...To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams(RCCDs),mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring artificial boundary(VSAB) is adopted to simulate the radiation damping of their infinite foundations, and based on the Marc software, a simplified seismic motion input method is presented by the equivalent nodal loads. Finally, based on the practical engineering of a RCC gravity dam, effects of radiation damping and construction interfaces on the dynamic characteristics of dams are investigated in detail. Analysis results show that dynamic response of the RCC gravity dam significantly reduces about 25% when the radiation damping of infinite foundation is considered. Hot interfaces and the normal cold interfaces have little influence on the dynamic response of the RCC gravity dam.However, nonlinear fracture along the cold interfaces at the dam heel will occur under the designed earthquake if the cold interfaces are combined poorly. Therefore, to avoid the fractures along the construction interfaces under the potential super earthquakes,combination quality of the RCC layers should be significantly ensured.展开更多
A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can e...A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.展开更多
Using the idea of general resonant triad of the hydrodynamic stability, the theoretical models for coherent structures in the wall region of a turbulent boundary layer is proposed. The interaction between coherent str...Using the idea of general resonant triad of the hydrodynamic stability, the theoretical models for coherent structures in the wall region of a turbulent boundary layer is proposed. The interaction between coherent structures in the wall region of a turbulent boundary layer is studied by combining the compact finite differences of high numerical accuracy and the Fourier spectral hybrid method for solving the three dimensional Navier Stokes equations. In this method, the third order mixed explicit implicit scheme is employed for the time integration. The fifth order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth order center compact schemes for the derivatives in spectral space are descried, respectively. The fourth order compact schemes satisfied by the velocities and pressure in spectral space is derived. As an application, the method is implemented to the wall region of a turbulent boundary to study the interaction between coherent structures. It is found that the numerical results are satisfactory.展开更多
The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, w...The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution. of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition I determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier-Stokes equations.展开更多
The objectives of this study are carried out a series of controlled large wave flume experiments using fine-grained sediment from the Huanghe River Delta,exploring the complete sequence of sediment behavior in the bot...The objectives of this study are carried out a series of controlled large wave flume experiments using fine-grained sediment from the Huanghe River Delta,exploring the complete sequence of sediment behavior in the bottom boundary layer(BBL)during wave-induced liquefaction.The results show that:(1)The BBL in silty seabed is exposed to a progressive wave,goes through a number of different stages including compaction before liquefaction,sediment liquefaction,and compaction after liquefaction,which determines the range and thickness of BBL.(2)With the introduction of waves,first,the sediment surface has settled by an amount S(S=1–2 cm)in the course of wave loadings with an insufficient accumulation of pore water pressure.And a thin high concentration layer formed the near-bed bottom.(3)Once the liquefaction sets in,the liquefied sediment with an‘orbital motion’and the sub-liquefied sediment form a two-layer-sediment region.The range of BBL extends downwards and stopped at a certain depth,subsequently,develops upwards with the compaction process.Meanwhile,resuspended sediments diffuse to the upper water column.(4)During the dynamics process of the BBL beneath progressive waves,the re-suspended sediment increment ranked as sediment liquefaction>erosion before liquefaction>compaction after liquefaction.展开更多
The microstructure of an explosively compacted Nd-Fe-B permanent magnet（Nd-Fe-B） was investigated by means of TEM and XRD. It is shown that there are three kinds of phases: Nd2Fe14B matrix phase, O-rich phases and N...The microstructure of an explosively compacted Nd-Fe-B permanent magnet（Nd-Fe-B） was investigated by means of TEM and XRD. It is shown that there are three kinds of phases: Nd2Fe14B matrix phase, O-rich phases and Nd-rich phase with different structures and compositions in the magnet. The hard magnetic phase Nd2Fe14B is tetragonal, which lattice parameters are determined to be a=0.88 nm and c=1.22 nm. The O-rich phase locates at the grain boundaries and the triple junctions has fcc structure whose lattice parameter is a=0.559 nm. A dislocation is observed in this phase. It is also found that a large number of the block-shaped Nd-rich phases with hcp structure are embedded in the Nd2Fe14B matrix or at grain boundary. Their lattice parameters are determined to be a=0.395 nm and c=0.628 nm.展开更多
文摘In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformation. Then, a fourth order compact difference scheme is proposed to solve the transformed elliptic equation on uniform girds. After that, a multigrid method is employed to solve the linear algebraic system arising from the difference equation. At last, the numerical experiments on some elliptic problems with interior/boundary layers are conducted to show high accuracy and high efficiency of the present method.
基金The research is supported by the National Natural Science Foundation of China(No.11671081)the Fundamental Research Funds for the Central Universities(No.242017K41044).
文摘In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.
文摘In the present work, we numerically study the laminar natural convection of a nanofluid confined in a square cavity. The vertical walls are assumed to be insulated, non-conducting, and impermeable to mass transfer. The horizontal walls are differentially heated, and the low is maintained at hot condition (sinusoidal) when the high one is cold. The objective of this work is to develop a new height accurate method for solving heat transfer equations. The new method is a Fourth Order Compact (F.O.C). This work aims to show the interest of the method and understand the effect of the presence of nanofluids in closed square systems on the natural convection mechanism. The numerical simulations are performed for Prandtl number ( ), the Rayleigh numbers varying between and for different volume fractions varies between 0% and 10% for the nanofluid (water + Cu).
文摘Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.
基金Project(51301150)supported by the National Natural Science Foundation of ChinaProject(2013KJXX-11)supported by the Special Program of Youth New-star of Science and Technology of Shaanxi Province,ChinaProject(Physics-2012SXTS05)supported by the High-level University Construction Special Program of Shaanxi Province,China
文摘The internal friction behavior of Al green power compact duxing the sintering process was studied as a function of temperature. The internal friction measurements were performed from room temperature to 600 °C. Two typical internal friction peaks were detected corresponding to heating and cooling processes, respectively. The heating peak corresponds to a recrystallization process of deformed Al particles, which is influenced by many extrinsic parameters, such as measuring frequency, strain amplitude, heating rate, power particle size and compacting pressure. However, the intrinsic nature of the peak is originated from the micro-sliding of the weak-bonding interfaces between Al particles and increased dislocation density induced in compressing. The cooling peak with the activation energy of (1.64±0.06) eV is associated with the grain boundary relaxation, which can be interpreted as the viscous sliding of grain boundaries. The similar phenomena are also found in the Mg green powder compact.
基金Projects(20120094110005,20120094130003)supported by the Research Fund for the Doctoral Program of Higher Education of ChinaProjects(51379068,51139001,51279052,51209077,51179066)supported by the National Natural Science Foundation of China+1 种基金Project(NCET-11-0628)supported by the Program for New Century Excellent Talents in University,ChinaProjects(201201038,201101013)supported by the Public Welfare Industry Research Special Fund Project of Ministry of Water Resources of China
文摘To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams(RCCDs),mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring artificial boundary(VSAB) is adopted to simulate the radiation damping of their infinite foundations, and based on the Marc software, a simplified seismic motion input method is presented by the equivalent nodal loads. Finally, based on the practical engineering of a RCC gravity dam, effects of radiation damping and construction interfaces on the dynamic characteristics of dams are investigated in detail. Analysis results show that dynamic response of the RCC gravity dam significantly reduces about 25% when the radiation damping of infinite foundation is considered. Hot interfaces and the normal cold interfaces have little influence on the dynamic response of the RCC gravity dam.However, nonlinear fracture along the cold interfaces at the dam heel will occur under the designed earthquake if the cold interfaces are combined poorly. Therefore, to avoid the fractures along the construction interfaces under the potential super earthquakes,combination quality of the RCC layers should be significantly ensured.
基金Project supported by the National Natural Science Foundation of China (Nos. 10172015 and 90205010)
文摘A new method was proposed for constructing total variation diminishing （TVD） upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD （CTVD） schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.
文摘Using the idea of general resonant triad of the hydrodynamic stability, the theoretical models for coherent structures in the wall region of a turbulent boundary layer is proposed. The interaction between coherent structures in the wall region of a turbulent boundary layer is studied by combining the compact finite differences of high numerical accuracy and the Fourier spectral hybrid method for solving the three dimensional Navier Stokes equations. In this method, the third order mixed explicit implicit scheme is employed for the time integration. The fifth order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth order center compact schemes for the derivatives in spectral space are descried, respectively. The fourth order compact schemes satisfied by the velocities and pressure in spectral space is derived. As an application, the method is implemented to the wall region of a turbulent boundary to study the interaction between coherent structures. It is found that the numerical results are satisfactory.
文摘The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution. of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition I determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier-Stokes equations.
基金The National Natural Science Foundation of China under contract Nos 41427803 and 41807229the Joint Fund of NSFC and Marine Science Research Centers of Shandong Province of China under contract No.U1606401China Geological Survey Program under contract No.121201006000182401。
文摘The objectives of this study are carried out a series of controlled large wave flume experiments using fine-grained sediment from the Huanghe River Delta,exploring the complete sequence of sediment behavior in the bottom boundary layer(BBL)during wave-induced liquefaction.The results show that:(1)The BBL in silty seabed is exposed to a progressive wave,goes through a number of different stages including compaction before liquefaction,sediment liquefaction,and compaction after liquefaction,which determines the range and thickness of BBL.(2)With the introduction of waves,first,the sediment surface has settled by an amount S(S=1–2 cm)in the course of wave loadings with an insufficient accumulation of pore water pressure.And a thin high concentration layer formed the near-bed bottom.(3)Once the liquefaction sets in,the liquefied sediment with an‘orbital motion’and the sub-liquefied sediment form a two-layer-sediment region.The range of BBL extends downwards and stopped at a certain depth,subsequently,develops upwards with the compaction process.Meanwhile,resuspended sediments diffuse to the upper water column.(4)During the dynamics process of the BBL beneath progressive waves,the re-suspended sediment increment ranked as sediment liquefaction>erosion before liquefaction>compaction after liquefaction.
基金Project(50071035) supported by the National Natural Science Foundation of China Project(02ZE14054) supported bythe Natural Science Foundation of Shanghai China
文摘The microstructure of an explosively compacted Nd-Fe-B permanent magnet（Nd-Fe-B） was investigated by means of TEM and XRD. It is shown that there are three kinds of phases: Nd2Fe14B matrix phase, O-rich phases and Nd-rich phase with different structures and compositions in the magnet. The hard magnetic phase Nd2Fe14B is tetragonal, which lattice parameters are determined to be a=0.88 nm and c=1.22 nm. The O-rich phase locates at the grain boundaries and the triple junctions has fcc structure whose lattice parameter is a=0.559 nm. A dislocation is observed in this phase. It is also found that a large number of the block-shaped Nd-rich phases with hcp structure are embedded in the Nd2Fe14B matrix or at grain boundary. Their lattice parameters are determined to be a=0.395 nm and c=0.628 nm.
