In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the diver...In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.展开更多
A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions a...A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.展开更多
This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of th...We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.展开更多
This article is concerned with the existence of maximal attractors in Hi (i = 1, 2, 4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn i...This article is concerned with the existence of maximal attractors in Hi (i = 1, 2, 4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3). One of the important features is that the metric spaces H(1), H(2), and H(4) we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ(4) H(i) (i = 1, 2, 4) is found, and the existence of maximal (universal) attractors in Hδ(i) (i = 1.2.4) is established.展开更多
In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initia...In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial data.展开更多
This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.
The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given...The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Differential quadrature method based on Fourier expansion basis to obtain a system of ordinary differential equation (ODE) then we implement the numerical scheme by computer programing and perform numerical solution. Finally the validation of the present scheme is demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produces a good result as compared to other researcher’s result and even generates a value at the nodes or mesh points that the results have not seen yet.展开更多
We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous...We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.展开更多
In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis o...In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system.We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions.It is shown that the solution exhibits a generalized Huygens principle.展开更多
In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ((φ(ρ))xxφ′(ρ))x with φ(ρ) = ρα. The model co...In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ((φ(ρ))xxφ′(ρ))x with φ(ρ) = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] (α=1/2) to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.展开更多
In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split i...In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.展开更多
Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to so...Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped.展开更多
We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectl...We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.展开更多
This paper is concerned with the pressureless Euler equations with viscous and flux perturbations.The existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is obtained....This paper is concerned with the pressureless Euler equations with viscous and flux perturbations.The existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is obtained.We show the stability of the delta wave of the pressureless Euler equations to the perturbations;that is,the limit solution of the pressureless Euler equations with viscous and flux perturbations is the delta wave solution of the pressureless Euler equations as the viscous and flux perturbation simultaneously vanish in the case u_(-)> u_(+).展开更多
Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direc...Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.展开更多
In this paper, we implement energy equation coupled with viscous Burgers’ equation as a mathematical model for the estimation of thermal pollution of river water. The model is a nonlinear system of partial differenti...In this paper, we implement energy equation coupled with viscous Burgers’ equation as a mathematical model for the estimation of thermal pollution of river water. The model is a nonlinear system of partial differential equations (PDEs) that read as an initial and boundary value problem (IBVP). For the numerical solution of the IBVP, we investigate an explicit second-order Lax- Wendroff type scheme for nonlinear parabolic PDEs. We present the numerical solutions graphically as a temperature profile, which shows good qualitative agreement with natural phenomena of heat transfer. We estimate the thermal pollution of water caused by industrialization on the bank of a river.展开更多
With the advantages of noncontact,high accuracy,and high flexibility,optical tweezers hold huge potential for micro-manipulation and force measurement.However,the majority of previous research focused on the state of ...With the advantages of noncontact,high accuracy,and high flexibility,optical tweezers hold huge potential for micro-manipulation and force measurement.However,the majority of previous research focused on the state of the motion of particles in the optical trap,but paid little attention to the early dynamic process between the initial state of the particles and the optical trap.Note that the viscous forces can greatly affect the motion of micro-spheres.In this paper,based on the equations of Newtonian mechanics,we investigate the dynamics of laser-trapped micro-spheres in the surrounding environment with different viscosity coefficients.Through the calculations,over time the particle trajectory clearly reveals the subtle details of the optical capture process,including acceleration,deceleration,turning,and reciprocating oscillation.The time to equilibrium mainly depends on the corresponding damping coefficient of the surrounding environment and the oscillation frequency of the optical tweezers.These studies are essential for understanding various mechanisms to engineer the mechanical motion behavior of molecules or microparticles in liquid or air.展开更多
In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate seri...In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.展开更多
A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling mode...A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling modes are dis-cussed.To treat the shock wave,the nonconservative coupling mode automatically switch to conservative coupling mode to preserve the conservative property when discontinuities pass through the artificial interface.To maintain the accuracy of the hybrid methods,the Lagrange interpolation polynomials and their derivatives are reconstructed to handle the coupling cells in the DDG subdomain,while the values of ghost points for the CD subdomain are calculated by the approximate polynomials from the DDG methods.The linear stabilities of these methods are demonstrated in detail through von-Neumann analysis.The multidomain hybrid DDG and CD meth-ods are then extended to one-and two-dimensional hyperbolic-parabolic equations.Numerical results validate that the multidomain hybrid methods are high-order ac-curate in the smooth regions,robust for viscous shock simulations and capable to save computational cost.展开更多
基金supported by the NSFC Grant 11901555,12271499the Cyrus Tang Foundationsupported by the NSFC Grant 11871448 and 12126604.
文摘In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.
基金Project (50975263) supported by the National Natural Science Foundation of ChinaProject (2010081015) supported by International Cooperation Project of Shanxi Province, China+1 种基金 Project (2010-78) supported by the Scholarship Council in Shanxi province, ChinaProject (2010420120005) supported by Doctoral Fund of Ministry of Education of China
文摘A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.
基金Supported by Natural Science Foundation of China (10471047)Natural Science Foundation of Guangdong Province (05300162)
文摘This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.
基金supported by"the Fundamental Research Funds for the Central Universities"
文摘We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.
基金supported in part by the NSF of China (10571024,10871040)the grant of Prominent Youth of Henan Province of China (0412000100)
文摘This article is concerned with the existence of maximal attractors in Hi (i = 1, 2, 4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3). One of the important features is that the metric spaces H(1), H(2), and H(4) we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ(4) H(i) (i = 1, 2, 4) is found, and the existence of maximal (universal) attractors in Hδ(i) (i = 1.2.4) is established.
基金The NSF (10125107) of China and partially supported by a Specific Foundation for Ph.D Specialities of Educational Department of China.
文摘In this paper we consider the viscous Cahn-Hilliard equation with spatial dimension n ≤ 5, and established global existence of weak solutions for small initial value and blow-up of solutions for any nontrivial initial data.
基金Qutstanding Youth Foundation (10125107) of China a Key Grant of the Ministry of Science and Technologies.
文摘This paper is devoted to viscous Cahn-Hiliiard equation with concentration dependent mobility. Some results on the existence, uniqueness and large time behavior are established.
文摘The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Differential quadrature method based on Fourier expansion basis to obtain a system of ordinary differential equation (ODE) then we implement the numerical scheme by computer programing and perform numerical solution. Finally the validation of the present scheme is demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produces a good result as compared to other researcher’s result and even generates a value at the nodes or mesh points that the results have not seen yet.
文摘We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.
文摘In this article,we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions(n≥4).We use the Green’s function method.Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system.We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions.It is shown that the solution exhibits a generalized Huygens principle.
文摘In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ((φ(ρ))xxφ′(ρ))x with φ(ρ) = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] (α=1/2) to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.
基金financially supported by the National Natural Science Foundation of China(Grant No.51349011)the Foundation of Si’chuan Educational Committee(Grant No.17ZB0452)+1 种基金the Innovation Team Project of Si’chuan Educational Committee(Grant No.18TD0019)the Longshan Academic Talent Research Support Program of the Southwest of Science and Technology(Grant Nos.18LZX715 and 18LZX410)
文摘In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
文摘Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped.
基金supported partially by NSFC(11671193,11971234)supported partially by the China Postdoctoral Science Foundation(2019M650581).
文摘We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient.The solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion limit.Moreover,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.
文摘This paper is concerned with the pressureless Euler equations with viscous and flux perturbations.The existence of Riemann solutions to the pressureless Euler equations with viscous and flux perturbations is obtained.We show the stability of the delta wave of the pressureless Euler equations to the perturbations;that is,the limit solution of the pressureless Euler equations with viscous and flux perturbations is the delta wave solution of the pressureless Euler equations as the viscous and flux perturbation simultaneously vanish in the case u_(-)> u_(+).
基金supported by the National Natural Science Foundation of China grants No.11971241.
文摘Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.
文摘In this paper, we implement energy equation coupled with viscous Burgers’ equation as a mathematical model for the estimation of thermal pollution of river water. The model is a nonlinear system of partial differential equations (PDEs) that read as an initial and boundary value problem (IBVP). For the numerical solution of the IBVP, we investigate an explicit second-order Lax- Wendroff type scheme for nonlinear parabolic PDEs. We present the numerical solutions graphically as a temperature profile, which shows good qualitative agreement with natural phenomena of heat transfer. We estimate the thermal pollution of water caused by industrialization on the bank of a river.
基金Project supported by the National Natural Science Foundation of China(Grant No.11804399)the Special Funds for Basic Scientific Research at the Central University of South-Central University for Nationalities(Grant No.CZQ20018)Special Funds for Basic Scientific Research at Central Universities(Grant No.YZZ17005)。
文摘With the advantages of noncontact,high accuracy,and high flexibility,optical tweezers hold huge potential for micro-manipulation and force measurement.However,the majority of previous research focused on the state of the motion of particles in the optical trap,but paid little attention to the early dynamic process between the initial state of the particles and the optical trap.Note that the viscous forces can greatly affect the motion of micro-spheres.In this paper,based on the equations of Newtonian mechanics,we investigate the dynamics of laser-trapped micro-spheres in the surrounding environment with different viscosity coefficients.Through the calculations,over time the particle trajectory clearly reveals the subtle details of the optical capture process,including acceleration,deceleration,turning,and reciprocating oscillation.The time to equilibrium mainly depends on the corresponding damping coefficient of the surrounding environment and the oscillation frequency of the optical tweezers.These studies are essential for understanding various mechanisms to engineer the mechanical motion behavior of molecules or microparticles in liquid or air.
基金Project supported by the National Natural Science Foundation of China (No. 10561151)the Basic Science Research Fund in the Universities Directly Under the Inner Mongolia Autonomous Region(No. JY20220003)the Scientific Research Project of Hetao College of China (No. HYZQ202122)。
文摘In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.
基金supported by the National Natural Science Foundation of China(Grant No.12001031).
文摘A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling modes are dis-cussed.To treat the shock wave,the nonconservative coupling mode automatically switch to conservative coupling mode to preserve the conservative property when discontinuities pass through the artificial interface.To maintain the accuracy of the hybrid methods,the Lagrange interpolation polynomials and their derivatives are reconstructed to handle the coupling cells in the DDG subdomain,while the values of ghost points for the CD subdomain are calculated by the approximate polynomials from the DDG methods.The linear stabilities of these methods are demonstrated in detail through von-Neumann analysis.The multidomain hybrid DDG and CD meth-ods are then extended to one-and two-dimensional hyperbolic-parabolic equations.Numerical results validate that the multidomain hybrid methods are high-order ac-curate in the smooth regions,robust for viscous shock simulations and capable to save computational cost.