This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse probl...This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.展开更多
In this paper,a new cracked stiffener model for the stiffener with a partthrough and open crack is proposed,considering the compatibility condition of displacements between the plate and the stiffener.Based on the fir...In this paper,a new cracked stiffener model for the stiffener with a partthrough and open crack is proposed,considering the compatibility condition of displacements between the plate and the stiffener.Based on the first-order shear deformation theory,the free vibration of stiffened isotropic plates with cracked stiffeners are investigated for the first time.The description of the crack parameters is based on the continuous equivalent bending stiffness and equivalent depth of the cracked beam,and it takes into consideration of shear deformation,bending-extensional coupling vibration,and eccentricity between the stiffeners and the plate.The stiffened plates with single or multiple cracked stiffeners are formulated and discussed.The Ritz method with the modified characteristic functions is applied to demonstrate the effects of crack parameters(crack depth and location)coupling with the position and number of the cracked stiffeners on the vibration frequencies and modes of the stiffened plate.The validity and accuracy of the present solutions are verified through convergence studies and compared with the finite element results.展开更多
A Nitsche-based element-free Galerkin(EFG)method for solving semilinear elliptic problems is developed and analyzed in this paper.The existence and uniqueness of the weak solution for semilinear elliptic problems are ...A Nitsche-based element-free Galerkin(EFG)method for solving semilinear elliptic problems is developed and analyzed in this paper.The existence and uniqueness of the weak solution for semilinear elliptic problems are proved based on a condition that the nonlinear term is an increasing Lipschitz continuous function of the unknown function.A simple iterative scheme is used to deal with the nonlinear integral term.We proved the existence,uniqueness and convergence of the weak solution sequence for continuous level of the simple iterative scheme.A commonly used assumption for approximate space,sometimes called inverse assumption,is proved.Optimal order error estimates in L 2 and H1 norms are proved for the linear and semilinear elliptic problems.In the actual numerical calculation,the characteristic distance h does not appear explicitly in the parameterβintroduced by the Nitsche method.The theoretical results are confirmed numerically。展开更多
In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solutio...In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solution is considered,which often generates a singular source and increases the difficulty of numerically solving the equation.The Crank-Nicolson technique,combined with the midpoint formula and the second-order convolution quadrature formula,is used for the time discretization.To increase the spatial accuracy,a fourth-order compact difference approximation,which is constructed by two compact difference operators,is adopted for spatial discretization.Then,the unconditional stability and convergence of the proposed scheme are strictly established with superlinear convergence accuracy in time and fourth-order accuracy in space.Finally,numerical experiments are given to support our theoretical results.展开更多
In this paper,we present a new vertex-centered arbitrary LagrangianEulerian(ALE)finite volume scheme for two-dimensional compressible flow.In our scheme,the momentum equation is discretized on the vertex control volum...In this paper,we present a new vertex-centered arbitrary LagrangianEulerian(ALE)finite volume scheme for two-dimensional compressible flow.In our scheme,the momentum equation is discretized on the vertex control volume,while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control volume.We attain the average of the fluid velocity on the vertex control volume directly by solving the conservation equations.Then we can obtain the fluid velocity at vertex with the reconstructed polynomial of the velocity.This fluid velocity is chosen as the mesh velocity,which makes the mesh move in a Lagrangian manner.Two WENO(Weighted Essentially Non-Oscillatory)reconstructions for the density(the total energy)and the velocity are used to make our scheme achieve the anticipated accuracy.Compared with the general vertexcentered schemes,our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large deformations.In addition,our scheme has good robustness,and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.展开更多
In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and dec...In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and decoupled,which greatly improve the computational efficiency.In order to resolve the time level mismatch of the discretization process,a special time marching method with high-order accuracy is constructed.Under the condition of slight time step constraints,the optimal error estimates of this method are given.Moreover,the theoretical results are verified by numerical experiments.Real simulations show the patterns of spots,rings,stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.展开更多
A computational code is developed for the numerical solution of onedimensional transient gas-liquid flows using drift-flux models,in isothermal and also with phase change situations.For these two-phase models,classica...A computational code is developed for the numerical solution of onedimensional transient gas-liquid flows using drift-flux models,in isothermal and also with phase change situations.For these two-phase models,classical upwind schemes such as Roe-and Godunov-type schemes are generally difficult to derive and expensive to use,since there are no treatable analytic expressions for the Jacobian matrix,eigenvalues and eigenvectors of the system of equations.On the other hand,the highorder compact finite difference scheme becomes an attractive alternative on these occasions,as it does not make use of any wave propagation information from the system of equations.The present paper extends the localized artificial diffusivity method for high-order compact finite difference schemes to solve two-phase flows with discontinuities.The numerical method has simple formulation,straightforward implementation,low computational cost and,most importantly,high-accuracy.The numerical methodology proposed is validated by solving several numerical examples given in the literature.The simulations are sixth-order accurate and it is shown that the proposed numerical method provides accurate approximations of shock waves and contact discontinuities.This is an essential property for simulations of realistic mass transport problems relevant to operations in the petroleum industry。展开更多
In the hybrid RANS-LES simulations,proper turbulent fluctuations should be added at the RANS-to-LES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible.Such t...In the hybrid RANS-LES simulations,proper turbulent fluctuations should be added at the RANS-to-LES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible.Such turbulence generation methods mostly need to know the distribution of the characteristic length scale of the background RANS model,which is important for the recovery process.The approximation of the length scale for the Spalart-Allmaras(S-A)model is not a trivial issue since the model’s one-equation nature.As a direct analogy,the approximations could be obtained from the definition of the Prandtl’s mixing length.Moreover,this paper proposes a new algebraic expression to approximate the intrinsic length scale of the S-A model.The underlying transportation mechanism of S-A model are largely exploited in the derivation of this new expression.The new proposed expression is employed in the generation of synthetic turbulence to perform the hybrid RANS-LES simulation of canonical wall-bounded turbulent flows.The comparisons demonstrated the feasibility and improved performance of the new length scale on generating synthetic turbulence at the LES inlet.展开更多
The meandering river is an unstable system with the characteristic of nonlinearity,which results from the instability of the flow and boundary.Focusing on the hydrodynamic nonlinearity of the bend,we use the weakly no...The meandering river is an unstable system with the characteristic of nonlinearity,which results from the instability of the flow and boundary.Focusing on the hydrodynamic nonlinearity of the bend,we use the weakly nonlinear theory and perturbation method to construct the nonlinear evolution equations of the disturbance amplitude and disturbance phase of two-dimensional flow in meandering bend.The influence of the curvature,Re and the disturbance wave number on the evolution of disturbance amplitude and disturbance phase are analyzed.Then,the spatial and temporal evolution of the disturbance vorticity is expounded.The research results show:that the curvature makes the flow more stable;that in the evolution of the disturbance amplitude effected by curvature,Re and the disturbance wave number,exist nonlinear attenuation with damping disturbances,and nonlinear explosive growth with positive disturbances;that the asymmetry distribution of the disturbance velocities increases with the curvature;that the location of the disturbance vorticity’s core area changes periodically with disturbance phase,and the disturbance vorticity gradually attenuates/increases with the decrease of the disturbance phase in the evolution process of damping/positive disturbances.These results shed light on the construction of the interaction model of hydrodynamic nonlinearity and geometric nonlinearity of bed.展开更多
In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection.For the time discretization,we apply a first-order convex splitti...In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection.For the time discretization,we apply a first-order convex splitting method and secondorder Crank-Nicolson scheme.For the space discretization,we utilize the Hessian recovery operator to approximate second-order derivatives of a C^(0)linear finite element function and hence the weak formulation of the fourth-order differential operator can be discretized in the linear finite element space.The energy-decay property of our proposed fully discrete schemes is rigorously proved.The robustness and the optimal-order convergence of the proposed algorithm are numerically verified.In a large spatial domain for a long period,we simulate coarsening dynamics,where 1/3-power-law is observed.展开更多
In this article,a new characteristic finite difference method is developed for solving miscible displacement problem in porous media.The new method combines the characteristic technique with mass-preserving interpolat...In this article,a new characteristic finite difference method is developed for solving miscible displacement problem in porous media.The new method combines the characteristic technique with mass-preserving interpolation,not only keeps mass balance but also is of second-order accuracy both in time and space.Numerical results are presented to confirm the convergence and the accuracy in time and space.展开更多
This paper presents a specific network architecture for approximation of the first Piola-Kirchhoff stress.The neural network enables us to construct the constitutive relation based on both macroscopic observations and...This paper presents a specific network architecture for approximation of the first Piola-Kirchhoff stress.The neural network enables us to construct the constitutive relation based on both macroscopic observations and atomistic simulation data.In contrast to traditional deep learning models,this architecture is intrinsic symmetric,guarantees the frame-indifference and material-symmetry of stress.Specifically,we build the approximation network inspired by the Cauchy-Born rule and virial stress formula.Several numerical results and theory analyses are presented to illustrate the learnability and effectiveness of our network.展开更多
Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics.During the past few decades,the method of fundamenta...Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics.During the past few decades,the method of fundamental solutions(MFS)has emerged as a popular and well-established meshless boundary collocation method for the numerical solution of many engineering applications.The classical MFS formulation,however,leads to dense and non-symmetric coefficient matrices which will be computationally expensive for large-scale engineering simulations.In this paper,a localized version of the MFS(LMFS)is devised for electroelastic analysis of twodimensional(2D)piezoelectric structures.In the LMFS,the entire computational domain is divided into a set of overlapping small sub-domains where the MFS-based approximation and the moving least square(MLS)technique are employed.Different to the classical MFS,the LMFS will produce banded and sparse coefficient matrices which makes the method very attractive for large-scale simulations.Preliminary numerical experiments illustrate that the present LMFM is very promising for coupled electroelastic analysis of piezoelectric materials.展开更多
In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure syste...In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.展开更多
In Zhu,Wang and Gao(SIAM J.Sci.Comput.,43(2021),pp.A3009–A3031),we proposed a new framework of troubled-cell indicator(TCI)using K-means clustering and the numerical results demonstrate that it can detect the trouble...In Zhu,Wang and Gao(SIAM J.Sci.Comput.,43(2021),pp.A3009–A3031),we proposed a new framework of troubled-cell indicator(TCI)using K-means clustering and the numerical results demonstrate that it can detect the troubled cells accurately using the KXRCF indication variable.The main advantage of this TCI framework is its great potential of extensibility.In this follow-up work,we introduce three more indication variables,i.e.,the TVB,Fu-Shu and cell-boundary jump indication variables,and show their good performance by numerical tests to demonstrate that the TCI framework offers great flexibility in the choice of indication variables.We also compare the three indication variables with the KXRCF one,and the numerical results favor the KXRCF and the cell-boundary jump indication variables.展开更多
In this paper,we present a quadratic auxiliary variable(QAV)technique to develop a novel class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation.The QAV approach is first utilized to...In this paper,we present a quadratic auxiliary variable(QAV)technique to develop a novel class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation.The QAV approach is first utilized to transform the original equation into a reformulated QAV system with a consistent initial condition.Then the reformulated QAV system is discretized by applying the Fourier pseudo-spectral method in space and the symplectic Runge-Kutta methods in time,which arrives at a class of fully discrete schemes.Under the consistent initial condition,they can be rewritten as a new fully discrete system by eliminating the introduced auxiliary variable,which is rigorously proved to be energy-preserving and symmetric.Ample numerical experiments are conducted to confirm the expected order of accuracy,conservative property and efficiency of the proposed methods.The presented numerical strategy makes it possible to directly apply a special class of Runge-Kutta methods to develop energy-preserving algorithms for a general conservative system with any polynomial energy.展开更多
This paper documents the first attempt to apply a localized method of fundamental solutions(LMFS)to the acoustic analysis of car cavity containing soundabsorbing materials.The LMFS is a recently developed meshless app...This paper documents the first attempt to apply a localized method of fundamental solutions(LMFS)to the acoustic analysis of car cavity containing soundabsorbing materials.The LMFS is a recently developed meshless approach with the merits of being mathematically simple,numerically accurate,and requiring less computer time and storage.Compared with the traditional method of fundamental solutions(MFS)with a full interpolation matrix,the LMFS can obtain a sparse banded linear algebraic system,and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains.In the LMFS,only circular or spherical fictitious boundary is involved.Based on these advantages,the method can be regarded as a competitive alternative to the standard method,especially for high-dimensional and large-scale problems.Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.展开更多
We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier.Based on the second-order finite...We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier.Based on the second-order finite-difference semidiscretization in the spatial direction,the integrating factor Runge-Kutta schemes are applied in the temporal direction.Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction,which is independent of the space step size.Finally,the theoretical analysis is verified by several numerical examples.展开更多
Imposing appropriate numerical boundary conditions at the symmetrical center r=0 is vital when computing compressible fluids with radial symmetry.Extrapolation and other traditional techniques are often employed,but s...Imposing appropriate numerical boundary conditions at the symmetrical center r=0 is vital when computing compressible fluids with radial symmetry.Extrapolation and other traditional techniques are often employed,but spurious numerical oscillations or wall-heating phenomena can occur.In this paper,we emphasize that because of the conservation property,the updating formula of the boundary cell average can coincide with the one for interior cell averages.To achieve second-order accuracy both in time and space,we associate obtaining the inner boundary value at r=0 with the resolution of the corresponding one-sided generalized Riemann problem(GRP).Acoustic approximation is applied in this process.It creates conditions to avoid the singularity of type 1/r and aids in obtaining the value of the singular quantity using L’Hospital’s rule.Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.展开更多
We have analyzed the kinetics of solid circular particles interacting with fluid,outer boundary and internal square shaped obstacles tilted at a 45°angle.The effects on the motion of particle due to collision wit...We have analyzed the kinetics of solid circular particles interacting with fluid,outer boundary and internal square shaped obstacles tilted at a 45°angle.The effects on the motion of particle due to collision with obstacles and wall are inspected.An Eulerian approach is used to study the behavior of particle in the fixed computational mesh.The interactions between fluid,particles and obstacles have been carried out in the whole domain by using fictitious boundary method(FBM).In this work,the particulate flow simulations are computed by using finite element solver FEATFLOW.Numerical results are presented by assigning different alignments to the obstacles and varying their positions in the domain.Particle-wall,particle-particle and particleobstacle collisions are treated by applying a modified collision model proposed by Glowinski et al.The rapid change in drag forces acting on obstacles due to nearby passing particles and its effect on the fluid motion has been investigated.展开更多
基金supported by the National Natural Science Foundation of China(No.12171036)Beijing Natural Science Foundation(No.Z210001)the NSF of China No.11971221,Guangdong NSF Major Fund No.2021ZDZX1001,the Shenzhen Sci-Tech Fund Nos.RCJC20200714114556020,JCYJ20200109115422828 and JCYJ20190809150413261,National Center for Applied Mathematics Shenzhen,and SUSTech International Center for Mathematics.
文摘This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.
基金supported by the national natural science foundation of China,project Nos.11972053 and 11772013。
文摘In this paper,a new cracked stiffener model for the stiffener with a partthrough and open crack is proposed,considering the compatibility condition of displacements between the plate and the stiffener.Based on the first-order shear deformation theory,the free vibration of stiffened isotropic plates with cracked stiffeners are investigated for the first time.The description of the crack parameters is based on the continuous equivalent bending stiffness and equivalent depth of the cracked beam,and it takes into consideration of shear deformation,bending-extensional coupling vibration,and eccentricity between the stiffeners and the plate.The stiffened plates with single or multiple cracked stiffeners are formulated and discussed.The Ritz method with the modified characteristic functions is applied to demonstrate the effects of crack parameters(crack depth and location)coupling with the position and number of the cracked stiffeners on the vibration frequencies and modes of the stiffened plate.The validity and accuracy of the present solutions are verified through convergence studies and compared with the finite element results.
基金supported by the Innovation Research Group Project in Universities of Chongqing of China(No.CXQT19018)the National Natural Science Foundation of China(Grant No.11971085)+1 种基金he Natural Science Foundation of Chongqing(Grant Nos.cstc2021jcyj-jqX0011 and cstc2020jcyj-msxm0777)an open project of Key Laboratory for Optimization and Control Ministry of Education,Chongqing Normal University(Grant No.CSSXKFKTM202006)。
文摘A Nitsche-based element-free Galerkin(EFG)method for solving semilinear elliptic problems is developed and analyzed in this paper.The existence and uniqueness of the weak solution for semilinear elliptic problems are proved based on a condition that the nonlinear term is an increasing Lipschitz continuous function of the unknown function.A simple iterative scheme is used to deal with the nonlinear integral term.We proved the existence,uniqueness and convergence of the weak solution sequence for continuous level of the simple iterative scheme.A commonly used assumption for approximate space,sometimes called inverse assumption,is proved.Optimal order error estimates in L 2 and H1 norms are proved for the linear and semilinear elliptic problems.In the actual numerical calculation,the characteristic distance h does not appear explicitly in the parameterβintroduced by the Nitsche method.The theoretical results are confirmed numerically。
基金supported by Natural Science Foundation of Jiangsu Province of China(Grant No.BK20201427)National Natural Science Foundation of China(Grant Nos.11701502 and 11871065)。
文摘In this paper,we present a linearized compact difference scheme for onedimensional time-space fractional nonlinear diffusion-wave equations with initial boundary value conditions.The initial singularity of the solution is considered,which often generates a singular source and increases the difficulty of numerically solving the equation.The Crank-Nicolson technique,combined with the midpoint formula and the second-order convolution quadrature formula,is used for the time discretization.To increase the spatial accuracy,a fourth-order compact difference approximation,which is constructed by two compact difference operators,is adopted for spatial discretization.Then,the unconditional stability and convergence of the proposed scheme are strictly established with superlinear convergence accuracy in time and fourth-order accuracy in space.Finally,numerical experiments are given to support our theoretical results.
基金supported by Natural Science Foundation of Guangdong province of China(Grant No.2018A030310038)National Natural Science Foundation of China(Grant Nos.11571002,11772067,11702028 and 12071046)。
文摘In this paper,we present a new vertex-centered arbitrary LagrangianEulerian(ALE)finite volume scheme for two-dimensional compressible flow.In our scheme,the momentum equation is discretized on the vertex control volume,while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control volume.We attain the average of the fluid velocity on the vertex control volume directly by solving the conservation equations.Then we can obtain the fluid velocity at vertex with the reconstructed polynomial of the velocity.This fluid velocity is chosen as the mesh velocity,which makes the mesh move in a Lagrangian manner.Two WENO(Weighted Essentially Non-Oscillatory)reconstructions for the density(the total energy)and the velocity are used to make our scheme achieve the anticipated accuracy.Compared with the general vertexcentered schemes,our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large deformations.In addition,our scheme has good robustness,and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.
基金supported by National Natural Science Foundation of China(Grant No.11801569)Natural Science Foundation of Shandong Province(CN)(Grant No.ZR2021MA001)the Fundamental Research Funds for the Central Universities(Grant Nos.22CX03025A and 22CX03020A).
文摘In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and decoupled,which greatly improve the computational efficiency.In order to resolve the time level mismatch of the discretization process,a special time marching method with high-order accuracy is constructed.Under the condition of slight time step constraints,the optimal error estimates of this method are given.Moreover,the theoretical results are verified by numerical experiments.Real simulations show the patterns of spots,rings,stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.
基金CAPES-National Council for the Improvement of Higher Education(Grant No.88882.435210/2019-01).
文摘A computational code is developed for the numerical solution of onedimensional transient gas-liquid flows using drift-flux models,in isothermal and also with phase change situations.For these two-phase models,classical upwind schemes such as Roe-and Godunov-type schemes are generally difficult to derive and expensive to use,since there are no treatable analytic expressions for the Jacobian matrix,eigenvalues and eigenvectors of the system of equations.On the other hand,the highorder compact finite difference scheme becomes an attractive alternative on these occasions,as it does not make use of any wave propagation information from the system of equations.The present paper extends the localized artificial diffusivity method for high-order compact finite difference schemes to solve two-phase flows with discontinuities.The numerical method has simple formulation,straightforward implementation,low computational cost and,most importantly,high-accuracy.The numerical methodology proposed is validated by solving several numerical examples given in the literature.The simulations are sixth-order accurate and it is shown that the proposed numerical method provides accurate approximations of shock waves and contact discontinuities.This is an essential property for simulations of realistic mass transport problems relevant to operations in the petroleum industry。
基金supported by National Key Research and Development Program of China(No.2019YFA0405201)National Natural Science Foundation of China(Nos.12002360 and 92052301)National Numerical Windtunnel project。
文摘In the hybrid RANS-LES simulations,proper turbulent fluctuations should be added at the RANS-to-LES interface to drive the numerical solution restoring to a physically resolved turbulence as rapidly as possible.Such turbulence generation methods mostly need to know the distribution of the characteristic length scale of the background RANS model,which is important for the recovery process.The approximation of the length scale for the Spalart-Allmaras(S-A)model is not a trivial issue since the model’s one-equation nature.As a direct analogy,the approximations could be obtained from the definition of the Prandtl’s mixing length.Moreover,this paper proposes a new algebraic expression to approximate the intrinsic length scale of the S-A model.The underlying transportation mechanism of S-A model are largely exploited in the derivation of this new expression.The new proposed expression is employed in the generation of synthetic turbulence to perform the hybrid RANS-LES simulation of canonical wall-bounded turbulent flows.The comparisons demonstrated the feasibility and improved performance of the new length scale on generating synthetic turbulence at the LES inlet.
基金supported by the National Natural Science Foundation of China(Grant Nos.51979185 and 51879182)。
文摘The meandering river is an unstable system with the characteristic of nonlinearity,which results from the instability of the flow and boundary.Focusing on the hydrodynamic nonlinearity of the bend,we use the weakly nonlinear theory and perturbation method to construct the nonlinear evolution equations of the disturbance amplitude and disturbance phase of two-dimensional flow in meandering bend.The influence of the curvature,Re and the disturbance wave number on the evolution of disturbance amplitude and disturbance phase are analyzed.Then,the spatial and temporal evolution of the disturbance vorticity is expounded.The research results show:that the curvature makes the flow more stable;that in the evolution of the disturbance amplitude effected by curvature,Re and the disturbance wave number,exist nonlinear attenuation with damping disturbances,and nonlinear explosive growth with positive disturbances;that the asymmetry distribution of the disturbance velocities increases with the curvature;that the location of the disturbance vorticity’s core area changes periodically with disturbance phase,and the disturbance vorticity gradually attenuates/increases with the decrease of the disturbance phase in the evolution process of damping/positive disturbances.These results shed light on the construction of the interaction model of hydrodynamic nonlinearity and geometric nonlinearity of bed.
基金supported by General Scientific Research Projects of Zhejiang Education Department(No.Y202147013)the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-Sen University(No.2021008)+1 种基金supported in part by NSFC Grant(No.12071496)Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.2020B1212060032)。
文摘In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection.For the time discretization,we apply a first-order convex splitting method and secondorder Crank-Nicolson scheme.For the space discretization,we utilize the Hessian recovery operator to approximate second-order derivatives of a C^(0)linear finite element function and hence the weak formulation of the fourth-order differential operator can be discretized in the linear finite element space.The energy-decay property of our proposed fully discrete schemes is rigorously proved.The robustness and the optimal-order convergence of the proposed algorithm are numerically verified.In a large spatial domain for a long period,we simulate coarsening dynamics,where 1/3-power-law is observed.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.22CX03020A).
文摘In this article,a new characteristic finite difference method is developed for solving miscible displacement problem in porous media.The new method combines the characteristic technique with mass-preserving interpolation,not only keeps mass balance but also is of second-order accuracy both in time and space.Numerical results are presented to confirm the convergence and the accuracy in time and space.
基金supported by the National Key Research and Development Program of China(No.2020YFA0714200)the National Nature Science Foundation of China(Nos.12125103 and 12071362)+1 种基金the Natural Science Foundation of Hubei Province(Nos.2021AAA010 and 2019CFA007)by the Fundamental Research Funds for the Central Universities.The numerical calculations have been done at the Super Computing Center of Wuhan University。
文摘This paper presents a specific network architecture for approximation of the first Piola-Kirchhoff stress.The neural network enables us to construct the constitutive relation based on both macroscopic observations and atomistic simulation data.In contrast to traditional deep learning models,this architecture is intrinsic symmetric,guarantees the frame-indifference and material-symmetry of stress.Specifically,we build the approximation network inspired by the Cauchy-Born rule and virial stress formula.Several numerical results and theory analyses are presented to illustrate the learnability and effectiveness of our network.
基金supported by the National Natural Science Foundation of China(Nos.11872220,12111530006)the Natural Science Foundation of Shandong Province of China(Nos.ZR2021JQ02,2019KJI009)the Key Laboratory of Road Construction Technology and Equipment(Chang’an University,No.300102251505).
文摘Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics.During the past few decades,the method of fundamental solutions(MFS)has emerged as a popular and well-established meshless boundary collocation method for the numerical solution of many engineering applications.The classical MFS formulation,however,leads to dense and non-symmetric coefficient matrices which will be computationally expensive for large-scale engineering simulations.In this paper,a localized version of the MFS(LMFS)is devised for electroelastic analysis of twodimensional(2D)piezoelectric structures.In the LMFS,the entire computational domain is divided into a set of overlapping small sub-domains where the MFS-based approximation and the moving least square(MLS)technique are employed.Different to the classical MFS,the LMFS will produce banded and sparse coefficient matrices which makes the method very attractive for large-scale simulations.Preliminary numerical experiments illustrate that the present LMFM is very promising for coupled electroelastic analysis of piezoelectric materials.
基金The first author would like to thank the support from the UM-Funded PhD Assistantship from University of MacaoThe second author was partially supported by Macao Young Scholar Program(AM201919)+5 种基金excellent youth project of Hunan Education Department(19B543)Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(2020ZYT003)The third author would like to thank financial support from National Natural Science Foundation of China(Grant Nos.11922120,11871489)FDCT of Macao SAR(Grant No.0082/2020/A2)University of Macao(Grant No.MYRG2020-00265-FST)Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications(Grant No.2020B1212030001).
文摘In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.
基金We thank the anonymous reviewers and the editor for their valuable comments and suggestions.The research of Z.Gao is partially supported by the National Key R&D Program of China(No.2021YFF0704002)The four authors,Z.Wang,Z.Gao,H.Wang and H.Zhu,want to acknowledge the funding support by NSFC grant No.11871443+3 种基金The research of Z.Wang and H.Zhu is also partially sponsored by NUPTSF(Grant No.NY220040)Natural Science Foundation of Jiangsu Province of China(No.BK20191375)Postgraduate Research&Practice Innovation Program of Jiangsu Province under Grant No.KYCX200787The research of Q.Zhang is partially supported by NSFC grant No.12071214.
文摘In Zhu,Wang and Gao(SIAM J.Sci.Comput.,43(2021),pp.A3009–A3031),we proposed a new framework of troubled-cell indicator(TCI)using K-means clustering and the numerical results demonstrate that it can detect the troubled cells accurately using the KXRCF indication variable.The main advantage of this TCI framework is its great potential of extensibility.In this follow-up work,we introduce three more indication variables,i.e.,the TVB,Fu-Shu and cell-boundary jump indication variables,and show their good performance by numerical tests to demonstrate that the TCI framework offers great flexibility in the choice of indication variables.We also compare the three indication variables with the KXRCF one,and the numerical results favor the KXRCF and the cell-boundary jump indication variables.
基金Yuezheng Gong’s work is partially supported by the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202002)the Fundamental Research Funds for the Central Universities(Grant No.NS2022070)+7 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220131)the National Natural Science Foundation of China(Grants Nos.12271252 and 12071216)Qi Hong’s work is partially supported by the National Natural Science Foundation of China(Grants No.12201297)the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202001)Chunwu Wang’s work is partially supported by Science Challenge Project(Grant No.TZ2018002)National Science and Technology Major Project(J2019-II-0007-0027)Yushun Wang’s work is partially supported by the National Key Research and Development Program of China(Grant No.2018YFC1504205)the National Natural Science Foundation of China(Grants No.12171245).
文摘In this paper,we present a quadratic auxiliary variable(QAV)technique to develop a novel class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation.The QAV approach is first utilized to transform the original equation into a reformulated QAV system with a consistent initial condition.Then the reformulated QAV system is discretized by applying the Fourier pseudo-spectral method in space and the symplectic Runge-Kutta methods in time,which arrives at a class of fully discrete schemes.Under the consistent initial condition,they can be rewritten as a new fully discrete system by eliminating the introduced auxiliary variable,which is rigorously proved to be energy-preserving and symmetric.Ample numerical experiments are conducted to confirm the expected order of accuracy,conservative property and efficiency of the proposed methods.The presented numerical strategy makes it possible to directly apply a special class of Runge-Kutta methods to develop energy-preserving algorithms for a general conservative system with any polynomial energy.
基金the National Natural Science Foundation of China(No.11802151)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA008).
文摘This paper documents the first attempt to apply a localized method of fundamental solutions(LMFS)to the acoustic analysis of car cavity containing soundabsorbing materials.The LMFS is a recently developed meshless approach with the merits of being mathematically simple,numerically accurate,and requiring less computer time and storage.Compared with the traditional method of fundamental solutions(MFS)with a full interpolation matrix,the LMFS can obtain a sparse banded linear algebraic system,and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains.In the LMFS,only circular or spherical fictitious boundary is involved.Based on these advantages,the method can be regarded as a competitive alternative to the standard method,especially for high-dimensional and large-scale problems.Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.
基金the National Key R&D Program of China(No.2020YFA0709800)the National Key Project(No.GJXM92579)the National Natural Science Foundation of China(No.12071481)。
文摘We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier.Based on the second-order finite-difference semidiscretization in the spatial direction,the integrating factor Runge-Kutta schemes are applied in the temporal direction.Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction,which is independent of the space step size.Finally,the theoretical analysis is verified by several numerical examples.
基金This work was partially supported by Science Challenge project TZ2016002NSFC with Nos.11771055,11671050,11871113,11871114,12026607,121710493D numerical simulation platform TB14-1 of the China Academy of Engineering Physics.
文摘Imposing appropriate numerical boundary conditions at the symmetrical center r=0 is vital when computing compressible fluids with radial symmetry.Extrapolation and other traditional techniques are often employed,but spurious numerical oscillations or wall-heating phenomena can occur.In this paper,we emphasize that because of the conservation property,the updating formula of the boundary cell average can coincide with the one for interior cell averages.To achieve second-order accuracy both in time and space,we associate obtaining the inner boundary value at r=0 with the resolution of the corresponding one-sided generalized Riemann problem(GRP).Acoustic approximation is applied in this process.It creates conditions to avoid the singularity of type 1/r and aids in obtaining the value of the singular quantity using L’Hospital’s rule.Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.
文摘We have analyzed the kinetics of solid circular particles interacting with fluid,outer boundary and internal square shaped obstacles tilted at a 45°angle.The effects on the motion of particle due to collision with obstacles and wall are inspected.An Eulerian approach is used to study the behavior of particle in the fixed computational mesh.The interactions between fluid,particles and obstacles have been carried out in the whole domain by using fictitious boundary method(FBM).In this work,the particulate flow simulations are computed by using finite element solver FEATFLOW.Numerical results are presented by assigning different alignments to the obstacles and varying their positions in the domain.Particle-wall,particle-particle and particleobstacle collisions are treated by applying a modified collision model proposed by Glowinski et al.The rapid change in drag forces acting on obstacles due to nearby passing particles and its effect on the fluid motion has been investigated.
