To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media,we derived conservation equations using the first-order perturbation approach and assuming stationary fluct...To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media,we derived conservation equations using the first-order perturbation approach and assuming stationary fluctuation fields of velocity and concentration.The concentration variance equation,similar to the mean concentration equation,consists of convection and dispersion terms with the mean water velocity and macrodispersivity.In addition,there is a production term in the concentration variance e-quation.The concentration variance production is quadratically proportional to the mean concentration gradient with a coefficient Qij,defined as the concentration variance productivity,which is the difference between the macrodispersivity Aij and the local dispersivity aij multiplied by a four-rank tensor.The macrodispersivity and the local dispersivity,respectively,result in the creation and dissipation of the concentration variance.The concentration variance is produced if the concentration gradient exists.For t→∞,Qij→0,which indicates that the creation and dissipation of the concentration variance are balanced at large travel time.We solve the variance equation numerically along with the mean e-quation using Aij,Qij,and the effective solute velocity v.The variance productivity increases with the decrease in transverse local dispersivity and is not sensitive to longitudinal local dispersivity.The maximum concentration variance occurs near the maximum mean concentration gradient.展开更多
Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis m...Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.展开更多
In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform...In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.展开更多
In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuou...An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.展开更多
We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conser...We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.展开更多
The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the ...The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.展开更多
This paper is devoted to the derivation of macroscopic fluid dynamics from the Boltzmann mesoscopic dynamics of a binary mixture of hard-sphere gas particles.Specifically the hydrodynamics limit is performed by employ...This paper is devoted to the derivation of macroscopic fluid dynamics from the Boltzmann mesoscopic dynamics of a binary mixture of hard-sphere gas particles.Specifically the hydrodynamics limit is performed by employing different time and space scalings.The paper shows that,depending on the magnitude of the parameters which define the scaling,the macroscopic quantities(number density,mean velocity and local temperature)are solutions of the acoustic equation,the linear incompressible Euler equation and the incompressible Navier–Stokes equation.The derivation is formally tackled by the recent moment method proposed by[C.Bardos,et al.,J.Stat.Phys.63(1991)323]and the results generalize the analysis performed in[C.Bianca,et al.,Commun.Nonlinear Sci.Numer.Simulat.29(2015)240].展开更多
In this paper, we consider the output feedback stabilization of a 1-D conservative wave equation, where the boundary velocity observation is subjected to a general disturbance. We first consider using only the output ...In this paper, we consider the output feedback stabilization of a 1-D conservative wave equation, where the boundary velocity observation is subjected to a general disturbance. We first consider using only the output of the system to online estimate the disturbance by active disturbance rejection control (ADRC). The observer is designed in terms of the disturbance estimator. Then we present an observer-based output feedback law to achieve stabilization. The estimated disturbance is proved to be convergent to the unknown disturbance and the velocity signal can be asymptotically recovered when time tends to infinity. At the same time, the asymptotic stability of the closed-loop system can be verified. Finally, some simulations are given to illustrate the theoretical conclusions.展开更多
We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-or...We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.展开更多
The history of forecasting wind waves by wave energy conservation equation Is briefly described. Several currently used wave numerical models for shallow water based on different wave theories are discussed. Wave ener...The history of forecasting wind waves by wave energy conservation equation Is briefly described. Several currently used wave numerical models for shallow water based on different wave theories are discussed. Wave energy conservation models for the simulation of shallow water waves are introduced, with emphasis placed on the SWAN model, which takes use of the most advanced wave research achievements and has been applied to several theoretical and field conditions. The characteristics and applicability of the model, the finite difference numerical scheme of the action balance equation and its source terms computing methods are described in detail. The model has been verified with the propagation refraction numerical experiments for waves propagating in following and opposing currents; finally, the model is applied to the Haian Gulf area to simulate the wave height and wave period field there, and the results are compared with observed data.展开更多
In the framework of the finite element method (FEM), a prediction method for the heating rate and the skin friction on a body surface is presented by using the energy and momentum conservation equations respectively. ...In the framework of the finite element method (FEM), a prediction method for the heating rate and the skin friction on a body surface is presented by using the energy and momentum conservation equations respectively. Meanwhile, a brief analysis is made of the role the weighted functions play in the present work.展开更多
Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and b...Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and biomedicine).At nanoscale,interfacial forces dominate over bulk forces,and nonlinear effects are important,which significantly deviate from conventional theory.During the past decades,a series of experiments,theories,and simulations have been performed to investigate fluid flow at nanoscale,which has advanced our fundamental knowledge of this topic.However,a critical review is still lacking,which has seriously limited the basic understanding of this area.Therefore herein,we systematically review experimental,theoretical,and simulation works on single-and multi-phases fluid flow at nanoscale.We also clearly point out the current research gaps and future outlook.These insights will promote the significant development of nonlinear flow physics at nanoscale and will provide crucial guidance on the relevant areas.展开更多
It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynami...It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.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
We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space...We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.展开更多
A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is pr...A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is proved in order O(h(2) + r(2)). In the proof, a new skill is used to deal with the term of difference quotient (e(j,k)(n))t. This is necessary, since there is no estimate of E(x, y, t) in L-infinity norm.展开更多
A systematic model development for oil flow in quasi-3D(1Dþ2D)is presented.Our approach provides a unified modeling scheme.Besides,additional terms are obtained,which allows for tubing area variation along the fl...A systematic model development for oil flow in quasi-3D(1Dþ2D)is presented.Our approach provides a unified modeling scheme.Besides,additional terms are obtained,which allows for tubing area variation along the flow direction.The area variation can be modeled as analytic function or random fluctuation,as it could be the result of deposits or tubing internal surface roughness.The proposed approach can be used to obtain analytic solutions which provide physical insight into the phenomena under scrutiny,including the validation of software tools,sensor development and sensor placement.One starts from conservation laws as given by kinetic theory and applies the transverse averaging technique(TAT)to extract the one-dimensional approximation in formal grounds.To demonstrate its application,the steady-state Ramey’s model,the Hasan’s transient model and a simple two-phase model are generated from the obtained equations.展开更多
The fractional single-phase-lagging(FSPL)heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging(SPL)heat conduction model.Based on the FSPL heat conduct...The fractional single-phase-lagging(FSPL)heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging(SPL)heat conduction model.Based on the FSPL heat conduction model,anomalous diffusion within a finite thin film is investigated.The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model.The analytical solution is obtained using Laplace transform method.The whole analysis is presented in dimensionless form.Numerical examples of particular interest have been studied and discussed in details.展开更多
This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model.The HLL Riemann solver is applied to solve the Riemann problem for the model equations.This sol...This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model.The HLL Riemann solver is applied to solve the Riemann problem for the model equations.This solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid mixture.Several representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical results.To demonstrate the robustness,effectiveness and capability of these methods,the model results are compared with reference solutions.In addition to that,these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the literature.The diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.展开更多
基金funded by NNSF of China and NSF-EPSCoR of University of Wyoming,USA.
文摘To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media,we derived conservation equations using the first-order perturbation approach and assuming stationary fluctuation fields of velocity and concentration.The concentration variance equation,similar to the mean concentration equation,consists of convection and dispersion terms with the mean water velocity and macrodispersivity.In addition,there is a production term in the concentration variance e-quation.The concentration variance production is quadratically proportional to the mean concentration gradient with a coefficient Qij,defined as the concentration variance productivity,which is the difference between the macrodispersivity Aij and the local dispersivity aij multiplied by a four-rank tensor.The macrodispersivity and the local dispersivity,respectively,result in the creation and dissipation of the concentration variance.The concentration variance is produced if the concentration gradient exists.For t→∞,Qij→0,which indicates that the creation and dissipation of the concentration variance are balanced at large travel time.We solve the variance equation numerically along with the mean e-quation using Aij,Qij,and the effective solute velocity v.The variance productivity increases with the decrease in transverse local dispersivity and is not sensitive to longitudinal local dispersivity.The maximum concentration variance occurs near the maximum mean concentration gradient.
基金Supported by the Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology under Grant No.YC150003
文摘Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.
文摘In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金supported in part by a“Computational R&D in Support of Stockpile Stewardship”Grant from Lawrence Livermore National Laboratorythe National Science Foundation Grants DMS-1619892+2 种基金the Air Force Office of Scientifc Research,USAF,under Grant/contract number FA9955012-0358the Army Research Office under Grant/contract number W911NF-15-1-0517the Spanish MCINN under Project PGC2018-097565-B-I00
文摘An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.
文摘We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.
文摘The conservative form and singular perturbed ordinary differential equation with periodic boundary value problem were studied, and a conservative difference scheme was constructed. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, it is proved that the scheme converges uniformly to the solution of differential equation with order one.
文摘This paper is devoted to the derivation of macroscopic fluid dynamics from the Boltzmann mesoscopic dynamics of a binary mixture of hard-sphere gas particles.Specifically the hydrodynamics limit is performed by employing different time and space scalings.The paper shows that,depending on the magnitude of the parameters which define the scaling,the macroscopic quantities(number density,mean velocity and local temperature)are solutions of the acoustic equation,the linear incompressible Euler equation and the incompressible Navier–Stokes equation.The derivation is formally tackled by the recent moment method proposed by[C.Bardos,et al.,J.Stat.Phys.63(1991)323]and the results generalize the analysis performed in[C.Bianca,et al.,Commun.Nonlinear Sci.Numer.Simulat.29(2015)240].
文摘In this paper, we consider the output feedback stabilization of a 1-D conservative wave equation, where the boundary velocity observation is subjected to a general disturbance. We first consider using only the output of the system to online estimate the disturbance by active disturbance rejection control (ADRC). The observer is designed in terms of the disturbance estimator. Then we present an observer-based output feedback law to achieve stabilization. The estimated disturbance is proved to be convergent to the unknown disturbance and the velocity signal can be asymptotically recovered when time tends to infinity. At the same time, the asymptotic stability of the closed-loop system can be verified. Finally, some simulations are given to illustrate the theoretical conclusions.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570the Open Foundation of State Key Laboratory of High Performance Computing of China+1 种基金the Research Fund of National University of Defense Technology under Grant No JC15-02-02the Fund from HPCL
文摘We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
基金"333"Project Scientific Research Foundation of Jiangsu ProvinceScience Fundation of Hohai University(3853)
文摘The history of forecasting wind waves by wave energy conservation equation Is briefly described. Several currently used wave numerical models for shallow water based on different wave theories are discussed. Wave energy conservation models for the simulation of shallow water waves are introduced, with emphasis placed on the SWAN model, which takes use of the most advanced wave research achievements and has been applied to several theoretical and field conditions. The characteristics and applicability of the model, the finite difference numerical scheme of the action balance equation and its source terms computing methods are described in detail. The model has been verified with the propagation refraction numerical experiments for waves propagating in following and opposing currents; finally, the model is applied to the Haian Gulf area to simulate the wave height and wave period field there, and the results are compared with observed data.
基金The project supported by the National Natural Science Foundation of China (19889210)
文摘In the framework of the finite element method (FEM), a prediction method for the heating rate and the skin friction on a body surface is presented by using the energy and momentum conservation equations respectively. Meanwhile, a brief analysis is made of the role the weighted functions play in the present work.
基金the funding support from the National Natural Science Foundation of China(51974013 and 11372033)the Open Research Foundation(NEPU-EOR-2019-003)the initiative funding from the University of Science and Technology Beijing.
文摘Fluid flow at nanoscale is closely related to many areas in nature and technology(e.g.,unconventional hydrocarbon recovery,carbon dioxide geo-storage,underground hydrocarbon storage,fuel cells,ocean desalination,and biomedicine).At nanoscale,interfacial forces dominate over bulk forces,and nonlinear effects are important,which significantly deviate from conventional theory.During the past decades,a series of experiments,theories,and simulations have been performed to investigate fluid flow at nanoscale,which has advanced our fundamental knowledge of this topic.However,a critical review is still lacking,which has seriously limited the basic understanding of this area.Therefore herein,we systematically review experimental,theoretical,and simulation works on single-and multi-phases fluid flow at nanoscale.We also clearly point out the current research gaps and future outlook.These insights will promote the significant development of nonlinear flow physics at nanoscale and will provide crucial guidance on the relevant areas.
文摘It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.
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Supported by Ministry of Science of Republic Serbia
文摘We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.
文摘A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is proved in order O(h(2) + r(2)). In the proof, a new skill is used to deal with the term of difference quotient (e(j,k)(n))t. This is necessary, since there is no estimate of E(x, y, t) in L-infinity norm.
基金partly funded by CNPq,Brazilian funding agency,and by PETROBRAS,Brazilian Oil Company.
文摘A systematic model development for oil flow in quasi-3D(1Dþ2D)is presented.Our approach provides a unified modeling scheme.Besides,additional terms are obtained,which allows for tubing area variation along the flow direction.The area variation can be modeled as analytic function or random fluctuation,as it could be the result of deposits or tubing internal surface roughness.The proposed approach can be used to obtain analytic solutions which provide physical insight into the phenomena under scrutiny,including the validation of software tools,sensor development and sensor placement.One starts from conservation laws as given by kinetic theory and applies the transverse averaging technique(TAT)to extract the one-dimensional approximation in formal grounds.To demonstrate its application,the steady-state Ramey’s model,the Hasan’s transient model and a simple two-phase model are generated from the obtained equations.
文摘The fractional single-phase-lagging(FSPL)heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging(SPL)heat conduction model.Based on the FSPL heat conduction model,anomalous diffusion within a finite thin film is investigated.The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model.The analytical solution is obtained using Laplace transform method.The whole analysis is presented in dimensionless form.Numerical examples of particular interest have been studied and discussed in details.
文摘This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical model.The HLL Riemann solver is applied to solve the Riemann problem for the model equations.This solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid mixture.Several representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical results.To demonstrate the robustness,effectiveness and capability of these methods,the model results are compared with reference solutions.In addition to that,these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the literature.The diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.
