A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the s...Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-bystep computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton-Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.展开更多
A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leave...A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.展开更多
For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a s...For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a structure-preserving method based on a discrete variational derivative method.Furthermore,to prevent the vertex concentration that may lead to numerical instability,we discretely introduce Deckelnick’s tangential velocity.Here,a modification term is introduced in the process of adding tangential velocity.This modified term enables the method to reproduce the equations’properties while preventing vertex concentration.Numerical experiments demonstrate that the proposed approach captures the equations’properties with high accuracy and avoids the concentration of vertices.展开更多
It was proved numerically that the Domain Decomposition Method CDDM) with one layer overlapping grids is identical to the block iterative method of linear algebra equations. The results obtained by using DDM could be ...It was proved numerically that the Domain Decomposition Method CDDM) with one layer overlapping grids is identical to the block iterative method of linear algebra equations. The results obtained by using DDM could be in reasonable agreement with the results of full-domain simulation. With the three dimensional solver developed by the authors, the flow field in a pipe was simulated by using the full-domain DDM with one layer overlapping grids and with patched grids respectively. Both of the two cases led to the convergent solution. Further research shows the superiority of the DDM with one layer overlapping grids to the DDM with patched grids. A comparison between the numerical results obtained by the authors and the experimental results given by Enayet[3] shows that the numerical results are reasonable.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
A hybrid numerical method for the hydraulic modeling of a curtain-walled dissipater of reflected waves from breakwaters is presented. In this method, a zonal approach that combines a nonlinear weakly dispersive wave (...A hybrid numerical method for the hydraulic modeling of a curtain-walled dissipater of reflected waves from breakwaters is presented. In this method, a zonal approach that combines a nonlinear weakly dispersive wave (Boussinesq-type equation) method and a Reynolds-Averaged Navier-Stokes (RANS) method is used. The Boussinesq-type equation is solved in the far field to describe wave transformation in shallow water. The RANS method is used in die near field to resolve the turbulent boundary layer and vortex flows around the structure. Suitable matching conditions are enforced at the interface between the viscous and the Boussinesq region. The Coupled RANS and Boussinesq method successfully resolves the vortex characteristics of flow in the vicinity of the structure, while unexpected phenomena like wave re-reflection are effectively controlled by lengthening the Boussinesq region. Extensive results on hydraulic performance of a curtain-walled dissipater and the mechanism of dissipation of reflected waves are presented, providing a reference for minimization of die breadth of the water chamber and for determination of the submerged depth of the curtain wall.展开更多
In this paper we consider numerical simulation of incompressible viscous flow in a infinite slip channel. Local artificial boundary conditions at an artificial boundary are derived by the continuity of velocity and no...In this paper we consider numerical simulation of incompressible viscous flow in a infinite slip channel. Local artificial boundary conditions at an artificial boundary are derived by the continuity of velocity and normal stress at the segment artificial boundary. The the original problem is reduced to a boundary value problem on a bounded computational domain. Numerical example shows that our artificial boundary conditions are very effective.展开更多
Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics ...Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.展开更多
A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative fi...A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.展开更多
The dry-gas seal has been widely used in different industries. With increased spin speed of the rotator shaft, turbulence occurs in the gas film between the stator and rotor seal faces. For the micro-scale flow in the...The dry-gas seal has been widely used in different industries. With increased spin speed of the rotator shaft, turbulence occurs in the gas film between the stator and rotor seal faces. For the micro-scale flow in the gas film and grooves, turbulence can change the pressure distribution of the gas film. Hence, the seal performance is influenced. However, turbulence effects and methods for their evaluation are not considered in the existing industrial designs of dry-gas seal. The present paper numerically obtains the turbulent flow fields of a spiral-groove dry-gas seal to analyze turbulence effects on seal performance. The direct numerical simulation （DNS） and Reynolds-averaged Navier-Stokes （RANS） methods are utilized to predict the velocity field properties in the grooves and gas film. The key performance parameter, open force, is obtained by integrating the pressure distribution, and the obtained result is in good agreement with the experimental data of other researchers. Very large velocity gradients are found in the sealing gas film because of the geometrical effects of the grooves. Considering turbulence effects, the calculation results show that both the gas film pressure and open force decrease. The RANS method underestimates the performance, compared with the DNS. The solution of the conventional Reynolds lubrication equation without turbulence effects suffers from significant calculation errors and a small application scope. The present study helps elucidate the physical mechanism of the hydrodynamic effects of grooves for improving and optimizing the industrial design or seal face pattern of a dry-gas seal.展开更多
A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the f...A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the finite analysis methods. In the present scheme, the finite analysis method is used to discretize the momentum equation and the MacCormack technique is used to discretize the continuity equation in a single grid system. The matrix of the discretized momentum equation is characterized by predominantly main diagonal elements, which ensures favorable convergence and stability for the numerical simulation by the combined method. To verify the present method, hydraulics simulation is carried out for a section down mainstream of the Huangpu River. The computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.展开更多
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
文摘Generally the incompressible viscous flow problem is described by the Navier-Stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-bystep computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton-Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.
基金Supported by the National Natural Science Foundation of China(11172134)the Funding of Jiangsu Innovation Program for Graduate Education(CXZZ110192)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.
基金This work was supported by JSPS KAKENHI Grant Nos.19K14590,21K18301,Japan.
文摘For fourth-order geometric evolution equations for planar curves with the dissipation of the bending energy,including the Willmore and the Helfrich flows,we consider a numerical approach.In this study,we construct a structure-preserving method based on a discrete variational derivative method.Furthermore,to prevent the vertex concentration that may lead to numerical instability,we discretely introduce Deckelnick’s tangential velocity.Here,a modification term is introduced in the process of adding tangential velocity.This modified term enables the method to reproduce the equations’properties while preventing vertex concentration.Numerical experiments demonstrate that the proposed approach captures the equations’properties with high accuracy and avoids the concentration of vertices.
文摘It was proved numerically that the Domain Decomposition Method CDDM) with one layer overlapping grids is identical to the block iterative method of linear algebra equations. The results obtained by using DDM could be in reasonable agreement with the results of full-domain simulation. With the three dimensional solver developed by the authors, the flow field in a pipe was simulated by using the full-domain DDM with one layer overlapping grids and with patched grids respectively. Both of the two cases led to the convergent solution. Further research shows the superiority of the DDM with one layer overlapping grids to the DDM with patched grids. A comparison between the numerical results obtained by the authors and the experimental results given by Enayet[3] shows that the numerical results are reasonable.
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.
基金This work was financially supported by the Trans-Century Training Program Fund for the Talent,Ministry of Education of China.
文摘A hybrid numerical method for the hydraulic modeling of a curtain-walled dissipater of reflected waves from breakwaters is presented. In this method, a zonal approach that combines a nonlinear weakly dispersive wave (Boussinesq-type equation) method and a Reynolds-Averaged Navier-Stokes (RANS) method is used. The Boussinesq-type equation is solved in the far field to describe wave transformation in shallow water. The RANS method is used in die near field to resolve the turbulent boundary layer and vortex flows around the structure. Suitable matching conditions are enforced at the interface between the viscous and the Boussinesq region. The Coupled RANS and Boussinesq method successfully resolves the vortex characteristics of flow in the vicinity of the structure, while unexpected phenomena like wave re-reflection are effectively controlled by lengthening the Boussinesq region. Extensive results on hydraulic performance of a curtain-walled dissipater and the mechanism of dissipation of reflected waves are presented, providing a reference for minimization of die breadth of the water chamber and for determination of the submerged depth of the curtain wall.
文摘In this paper we consider numerical simulation of incompressible viscous flow in a infinite slip channel. Local artificial boundary conditions at an artificial boundary are derived by the continuity of velocity and normal stress at the segment artificial boundary. The the original problem is reduced to a boundary value problem on a bounded computational domain. Numerical example shows that our artificial boundary conditions are very effective.
基金supported by the National Natural Science Foundation of China (No.10621062)the Research Fund for Next Generation of General Armament Department (No.9140A13050207KG29)
文摘Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.
文摘A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.
基金supported by Scientific Research Foundation for Returned Scholars,Ministry of Education of China
文摘The dry-gas seal has been widely used in different industries. With increased spin speed of the rotator shaft, turbulence occurs in the gas film between the stator and rotor seal faces. For the micro-scale flow in the gas film and grooves, turbulence can change the pressure distribution of the gas film. Hence, the seal performance is influenced. However, turbulence effects and methods for their evaluation are not considered in the existing industrial designs of dry-gas seal. The present paper numerically obtains the turbulent flow fields of a spiral-groove dry-gas seal to analyze turbulence effects on seal performance. The direct numerical simulation （DNS） and Reynolds-averaged Navier-Stokes （RANS） methods are utilized to predict the velocity field properties in the grooves and gas film. The key performance parameter, open force, is obtained by integrating the pressure distribution, and the obtained result is in good agreement with the experimental data of other researchers. Very large velocity gradients are found in the sealing gas film because of the geometrical effects of the grooves. Considering turbulence effects, the calculation results show that both the gas film pressure and open force decrease. The RANS method underestimates the performance, compared with the DNS. The solution of the conventional Reynolds lubrication equation without turbulence effects suffers from significant calculation errors and a small application scope. The present study helps elucidate the physical mechanism of the hydrodynamic effects of grooves for improving and optimizing the industrial design or seal face pattern of a dry-gas seal.
基金supported by the National Natural Science Foundation of China (Grant No.10572084)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20050280008)
文摘A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the finite analysis methods. In the present scheme, the finite analysis method is used to discretize the momentum equation and the MacCormack technique is used to discretize the continuity equation in a single grid system. The matrix of the discretized momentum equation is characterized by predominantly main diagonal elements, which ensures favorable convergence and stability for the numerical simulation by the combined method. To verify the present method, hydraulics simulation is carried out for a section down mainstream of the Huangpu River. The computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.
