To fundamentally alleviate the excavation chamber clogging during slurry tunnel boring machine(TBM)advancing in hard rock,large-diameter short screw conveyor was adopted to slurry TBM of Qingdao Jiaozhou Bay Second Un...To fundamentally alleviate the excavation chamber clogging during slurry tunnel boring machine(TBM)advancing in hard rock,large-diameter short screw conveyor was adopted to slurry TBM of Qingdao Jiaozhou Bay Second Undersea Tunnel.To evaluate the discharging performance of short screw conveyor in different cases,the full-scale transient slurry-rock two-phase model for a short screw conveyor actively discharging rocks was established using computational fluid dynamics-discrete element method(CFD-DEM)coupling approach.In the fluid domain of coupling model,the sliding mesh technology was utilized to describe the rotations of the atmospheric composite cutterhead and the short screw conveyor.In the particle domain of coupling model,the dynamic particle factories were established to produce rock particles with the rotation of the cutterhead.And the accuracy and reliability of the CFD-DEM simulation results were validated via the field test and model test.Furthermore,a comprehensive parameter analysis was conducted to examine the effects of TBM operating parameters,the geometric design of screw conveyor and the size of rocks on the discharging performance of short screw conveyor.Accordingly,a reasonable rotational speed of screw conveyor was suggested and applied to Jiaozhou Bay Second Undersea Tunnel project.The findings in this paper could provide valuable references for addressing the excavation chamber clogging during ultra-large-diameter slurry TBM tunneling in hard rock for similar future.展开更多
The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional ...The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional hydrocarbon reservoirs and associated hazards.Many coupling techniques have been developed to include the effects of fluid flow in the discrete element method(DEM),and the techniques have been applied to a variety of geomechanical problems.Although these coupling methods have been successfully applied in various engineering fields,no single fluid/DEM coupling method is universal due to the complexity of engineering problems and the limitations of the numerical methods.For researchers and engineers,the key to solve a specific problem is to select the most appropriate fluid/DEM coupling method among these modeling technologies.The purpose of this paper is to give a comprehensive review of fluid flow/DEM coupling methods and relevant research.Given their importance,the availability or unavailability of best practice guidelines is outlined.The theoretical background and current status of DEM are introduced first,and the principles,applications,and advantages and disadvantages of different fluid flow/DEM coupling methods are discussed.Finally,a summary with speculation on future development trends is given.展开更多
An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal str...An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.展开更多
This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on t...This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.展开更多
In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the line...In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.展开更多
A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in freque...A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.展开更多
The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin...The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.展开更多
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as th...A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.展开更多
Based on linearized 2-D Navier-Stokes equation, a Laplacetransform-boundary element coupling method for viscousfluid-structure impact analysis is proposed. Under assumption ofincompressibility for the fluid, the corre...Based on linearized 2-D Navier-Stokes equation, a Laplacetransform-boundary element coupling method for viscousfluid-structure impact analysis is proposed. Under assumption ofincompressibility for the fluid, the corresponding equivalentboundary integral equation in terms of the potential function andstream function is first established by Lamb's transform in theLaplace transform domain.展开更多
In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an al...In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.展开更多
This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress...This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.展开更多
Fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The b...Fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The bottom boundary of the microchannel is simulated by size-dependent beam elements for the finite element method （FEM） based on a modified cou- ple stress theory. The lattice Boltzmann method （LBM） using the D2Q13 LB model is coupled to the FEM in order to solve the fluid part of the FSI problem. Because of the fact that the LBM generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallel computing. The simulations are carried out on graphics processing units （GPUs） using computed unified device architecture （CUDA）. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.展开更多
In this paper, the domain integral of the form of Poisson equation is translatedinto complete boundary integral by the fundamental solution of higher-order Laplaceoperator, the dimensions of the problem can be contrac...In this paper, the domain integral of the form of Poisson equation is translatedinto complete boundary integral by the fundamental solution of higher-order Laplaceoperator, the dimensions of the problem can be contracted into one. The numericalexamples for Stokes equations show that this method is efficient.展开更多
In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful ...The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.展开更多
A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding tim...A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.展开更多
This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based ...This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.展开更多
A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The t...A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.展开更多
The multi-physics simulation of coupled fluid-structure interaction problems, with disjoint fluid and solid domains, requires one to choose a method for enforcing the fluid-structure coupling at the interface between ...The multi-physics simulation of coupled fluid-structure interaction problems, with disjoint fluid and solid domains, requires one to choose a method for enforcing the fluid-structure coupling at the interface between solid and fluid. While it is common knowledge that the choice of coupling technique can be very problem dependent, there exists no satisfactory coupling comparison methodology that allows for conclusions to be drawn with respect to the comparison of computational cost and solution accuracy for a given scenario. In this work, we develop a computational framework where all aspects of the computation can be held constant, save for the method in which the coupled nature of the fluid-structure equations is enforced. To enable a fair comparison of coupling methods, all simulations presented in this work are implemented within a single numerical framework within the deal.ii [1] finite element library. We have chosen the two-dimensional benchmark test problem of Turek and Hron [2] as an example to examine the relative accuracy of the coupling methods studied;however, the comparison technique is equally applicable to more complex problems. We show that for the specific case considered herein the monolithic approach outperforms partitioned and quasi-direct methods;however, this result is problem dependent and we discuss computational and modeling aspects which may affect other comparison studies.展开更多
In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for th...In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2023YJS053)the National Natural Science Foundation of China(Grant No.52278386).
文摘To fundamentally alleviate the excavation chamber clogging during slurry tunnel boring machine(TBM)advancing in hard rock,large-diameter short screw conveyor was adopted to slurry TBM of Qingdao Jiaozhou Bay Second Undersea Tunnel.To evaluate the discharging performance of short screw conveyor in different cases,the full-scale transient slurry-rock two-phase model for a short screw conveyor actively discharging rocks was established using computational fluid dynamics-discrete element method(CFD-DEM)coupling approach.In the fluid domain of coupling model,the sliding mesh technology was utilized to describe the rotations of the atmospheric composite cutterhead and the short screw conveyor.In the particle domain of coupling model,the dynamic particle factories were established to produce rock particles with the rotation of the cutterhead.And the accuracy and reliability of the CFD-DEM simulation results were validated via the field test and model test.Furthermore,a comprehensive parameter analysis was conducted to examine the effects of TBM operating parameters,the geometric design of screw conveyor and the size of rocks on the discharging performance of short screw conveyor.Accordingly,a reasonable rotational speed of screw conveyor was suggested and applied to Jiaozhou Bay Second Undersea Tunnel project.The findings in this paper could provide valuable references for addressing the excavation chamber clogging during ultra-large-diameter slurry TBM tunneling in hard rock for similar future.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41772286 and 42077247)the Fundamental Research Funds for the Central Universities, China
文摘The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional hydrocarbon reservoirs and associated hazards.Many coupling techniques have been developed to include the effects of fluid flow in the discrete element method(DEM),and the techniques have been applied to a variety of geomechanical problems.Although these coupling methods have been successfully applied in various engineering fields,no single fluid/DEM coupling method is universal due to the complexity of engineering problems and the limitations of the numerical methods.For researchers and engineers,the key to solve a specific problem is to select the most appropriate fluid/DEM coupling method among these modeling technologies.The purpose of this paper is to give a comprehensive review of fluid flow/DEM coupling methods and relevant research.Given their importance,the availability or unavailability of best practice guidelines is outlined.The theoretical background and current status of DEM are introduced first,and the principles,applications,and advantages and disadvantages of different fluid flow/DEM coupling methods are discussed.Finally,a summary with speculation on future development trends is given.
基金the National Metal and Materials Technology Centerthe Thailand Research Fund+1 种基金the Office of Higher Education Commissionthe Chulalongkorn University for supporting the present research
文摘An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.
基金supported by the National Natural Science Foundation of China (10771134).
文摘This paper presents a hybrid finite volume/finite element method for the incompressible generalized Newtonian fluid flow （Power-Law model）. The collocated （i.e. non-staggered） arrangement of variables is used on the unstructured triangular grids, and a fractional step projection method is applied for the velocity-pressure coupling. The cell-centered finite volume method is employed to discretize the momentum equation and the vertex-based finite element for the pressure Poisson equation. The momentum interpolation method is used to suppress unphysical pressure wiggles. Numerical experiments demonstrate that the current hybrid scheme has second order accuracy in both space and time. Results on flows in the lid-driven cavity and between parallel walls for Newtonian and Power-Law models are also in good agreement with the published solutions.
文摘In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.
文摘A boundary element method is presented for the coupled motionanalysis of structural vibration with small-amplitude fluid sloshingin two-dimensional space. The linearized Navier-Stokes equations areconsidered in frequency domain and transformed into boundary integralequations. An appropriate fundamental solution for the Helmholtzequation with pure imaginary constant is found. The condition ofzero-stress is imposed on the free surface, and non-slip condition offluid particles is Imposed on the walls of the container. For rigidmotion models, the expressions for added mass and Added damping tothe structural motion equations are obtained. Some typical numericalexamples are Presented.
文摘The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.
文摘A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
基金the National Defence Foundation of Science & Technology of China (No.J14.8.1.JW0515)
文摘Based on linearized 2-D Navier-Stokes equation, a Laplacetransform-boundary element coupling method for viscousfluid-structure impact analysis is proposed. Under assumption ofincompressibility for the fluid, the corresponding equivalentboundary integral equation in terms of the potential function andstream function is first established by Lamb's transform in theLaplace transform domain.
文摘In this paper, a new finite element method for the flow analysis of the viscous incompressible power-law fluid is proposed by the use of penalty-hybrid/mixed finite element formulation and by the introduction of an alternative perturbation, which is weighted by viscosity, of the continuity equation. A numerical example is presented to exhibit the efficiency of the method.
文摘This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.
文摘Fluid-structure interaction （FSI） problems in microchannels play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow in microchannel considering FSI. The bottom boundary of the microchannel is simulated by size-dependent beam elements for the finite element method （FEM） based on a modified cou- ple stress theory. The lattice Boltzmann method （LBM） using the D2Q13 LB model is coupled to the FEM in order to solve the fluid part of the FSI problem. Because of the fact that the LBM generally needs only nearest neighbor information, the algorithm is an ideal candidate for parallel computing. The simulations are carried out on graphics processing units （GPUs） using computed unified device architecture （CUDA）. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.
文摘In this paper, the domain integral of the form of Poisson equation is translatedinto complete boundary integral by the fundamental solution of higher-order Laplaceoperator, the dimensions of the problem can be contracted into one. The numericalexamples for Stokes equations show that this method is efficient.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
基金Project supported by the National Natural Science Foundation of China and the Natural Science Foundationof Zhejiang Province
文摘The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.
基金This project is financially supported by the National Education Foundation of China.
文摘A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.
文摘This work presents a new application for the Hierarchical Function Expansion Method for the solution of the Navier-Stokes equations for compressible fluids in two dimensions and in high velocity. This method is based on the finite elements method using the Petrov-Galerkin formulation, know as SUPG (Streamline Upwind Petrov-Galerkin), applied with the expansion of the variables into hierarchical functions. To test and validate the numerical method proposed as well as the computational program developed simulations are performed for some cases whose theoretical solutions are known. These cases are the following: continuity test, stability and convergence test, temperature step problem, and several oblique shocks. The objective of the last cases is basically to verify the capture of the shock wave by the method developed. The results obtained in the simulations with the proposed method were good both qualitatively and quantitatively when compared with the theoretical solutions. This allows concluding that the objectives of this work are reached.
基金Project supported by the National Natural Science Foundation of China (Nos.10302013,10572022)
文摘A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.
文摘The multi-physics simulation of coupled fluid-structure interaction problems, with disjoint fluid and solid domains, requires one to choose a method for enforcing the fluid-structure coupling at the interface between solid and fluid. While it is common knowledge that the choice of coupling technique can be very problem dependent, there exists no satisfactory coupling comparison methodology that allows for conclusions to be drawn with respect to the comparison of computational cost and solution accuracy for a given scenario. In this work, we develop a computational framework where all aspects of the computation can be held constant, save for the method in which the coupled nature of the fluid-structure equations is enforced. To enable a fair comparison of coupling methods, all simulations presented in this work are implemented within a single numerical framework within the deal.ii [1] finite element library. We have chosen the two-dimensional benchmark test problem of Turek and Hron [2] as an example to examine the relative accuracy of the coupling methods studied;however, the comparison technique is equally applicable to more complex problems. We show that for the specific case considered herein the monolithic approach outperforms partitioned and quasi-direct methods;however, this result is problem dependent and we discuss computational and modeling aspects which may affect other comparison studies.
文摘In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.
