This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employ...This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employed in conjunction with either the Jacobi or the Gauss-Seidel iteration process, one can obtain computed solutions that are accurate and free of unphysical展开更多
In this paper,we develop a fourth-order conservative wavelet-based shock-capturing scheme.The scheme is constructed by combining a wavelet collocation upwind method with the monotonic tangent of hyperbola for interfac...In this paper,we develop a fourth-order conservative wavelet-based shock-capturing scheme.The scheme is constructed by combining a wavelet collocation upwind method with the monotonic tangent of hyperbola for interface capturing(THINC)technique.We employ boundary variation diminishing(BVD)reconstruction to enhance the scheme’s effectiveness in handling shocks.First,we prove that wavelet collocation upwind schemes based on interpolating wavelets can be reformulated into a conservative form within the framework of wavelet theory,forming the foundation of the proposed scheme.The new fourthorder accurate scheme possesses significantly better spectral resolution than the fifth-and even seventh-order WENO-Z(weighted essentially non-oscillatory)schemes over the entire wave-number range.Moreover,the inherent low-pass filtering property of the wavelet bases allows them to filter high-frequency numerical oscillations,endowing the wavelet upwind scheme with robustness and accuracy in solving problems under extreme conditions.Notably,due to the wavelet multiresolution approximation,the proposed scheme possesses a distinctive shape-preserving property absent in the WENO-Z schemes and the fifth-order schemes with BVD reconstruction based on polynomials.Furthermore,compared to the fifth-order scheme with BVD reconstruction based on polynomials—which is significantly superior to the WENO schemes—the proposed scheme further enhances the ability to capture discontinuities.展开更多
In this paper,we present a new fourth-order upwinding embedded boundary method(UEBM)over Cartesian grids,originally proposed in the Journal of Computational Physics[190(2003),pp.159-183.]as a second-order method for t...In this paper,we present a new fourth-order upwinding embedded boundary method(UEBM)over Cartesian grids,originally proposed in the Journal of Computational Physics[190(2003),pp.159-183.]as a second-order method for treating material interfaces for Maxwell’s equations.In addition to the idea of the UEBM to evolve solutions at interfaces,we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces.As a result,Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method,in contrast to the original second-order UEBM based on a Lax-Wendroff type difference.The final scheme allows time step sizes independent of the interface locations.Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method.We tested the scheme for several wave problems with various material interface locations,including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis.展开更多
In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow e...In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.展开更多
It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth ...It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.展开更多
The computational fluid dynamics （CFD） method is used to investigate the aerodynamic characteristics of the seat/occupant with windblast protection devices. The upwind Osher scheme is used for the spatial discretisa...The computational fluid dynamics （CFD） method is used to investigate the aerodynamic characteristics of the seat/occupant with windblast protection devices. The upwind Osher scheme is used for the spatial discretisation. The detached-eddy simulation （DES） based on the Spalart-Allmaras one-equation turbulence model is ap- plied to the detached viscous flow simulation behind the seat/occupant, with Mach numbers 0.6 and 1.2 at attack angles between --10 and 30°, and at two sideslip angles of 0 and 15°, respectively. The aerodynamic characteristics of seat/occupants with and without windblast protection devices are calculated in cases of the freestream Mach numbers 0. 8 and 1.6, attack angles from 5 to 30°, and three sideslip angles of 0, --20 and --50°, respectively. Results show that simulation results agree well with experimental data. And the occupant is efficiently protected by windblast protection devices.展开更多
Adaptive Delaunay triangulation is combined with the cell-centered upwinding algorithm to analyze inviscid high-speed compressible flow problems. The multidimensional dissipation scheme was developed and included in t...Adaptive Delaunay triangulation is combined with the cell-centered upwinding algorithm to analyze inviscid high-speed compressible flow problems. The multidimensional dissipation scheme was developed and included in the upwinding algorithm for unstructured triangular meshes to improve the computed shock wave resolution. The solution accuracy is further improved by coupling an error estimation procedure to a remeshing algorithm that generates small elements in regions with large change of solution gradients, and at the same time, larger elements in other regions. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. Efficiency of the combined procedure is evaluated by analyzing supersonic shocks and shock propagation behaviors for both the steady and unsteady high-speed compressible flows.展开更多
A parallelized upwind flux splitting scheme for supersonic reacting flows on hybrid meshes is presented. The complexity of super/hyper-sonic combustion flows makes it necessary to establish solvers with higher resolut...A parallelized upwind flux splitting scheme for supersonic reacting flows on hybrid meshes is presented. The complexity of super/hyper-sonic combustion flows makes it necessary to establish solvers with higher resolution and efficiency for multi-component Euler/N-S equations. Hence, a spatial second-order van Leer type flux vector splitting scheme is established by introducing auxiliary points in interpolation, and a domain decomposition method used on unstructured hybrid meshes for obtaining high calculating efficiency. The numerical scheme with five-stage Runge-Kutta time step method is implemented to the simulation of combustion flows, including the supersonic hydrogen/air combustion and the normal injection of hydrogen into reacting flows. Satisfying results are obtained compared with limited references.展开更多
A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around...A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes（RANS） equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method＂ and ‘‘minimum distance scheme of donor elements method＂ are established in this work. To improve the computational efficiency, Message Passing Interface（MPI） parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage（FAS） multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.展开更多
To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficu...To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method （FEM） algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin （SUPG） weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations （Reynolds equation）. A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals＇ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.展开更多
Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi...Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.展开更多
In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the...In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.展开更多
A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and...A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.展开更多
The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence. The mathematical model of the problem and upwind splitting alternating direction method w...The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence. The mathematical model of the problem and upwind splitting alternating direction method were presented. Using this method, the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Provivce was finished. The numerical results turned out to be identical with the real measurements, so the prediction of the consequences of protection projectects is reasonable.展开更多
The simulation of hypersonic flows with fully unstructured(tetrahedral)grids has severe problems with respect to the prediction of stagnation region heating,due to the random face orientation without alignment to the ...The simulation of hypersonic flows with fully unstructured(tetrahedral)grids has severe problems with respect to the prediction of stagnation region heating,due to the random face orientation without alignment to the bow shock.To improve the accuracy of aero-heating predictions,three multi-dimensional approaches on unstructured grids are coupled in our Reynolds-averaged Navier-Stokes(RANS)solver,including multi-dimensional upwind flux reconstruction(MUP),multi-dimensional limiter(MLP-u2)and multi-dimensional gradient reconstruction(MLR).The coupled multi-dimensional RANS solver is validated by several typical verification and validation(V&V)cases,including hypersonic flows over a cylinder,a blunt biconic,and a double-ellipsoid,with commonly used prism/tetrahedral hybrid grids.Finally,the coupled multi-dimensional solver is applied to simulating the heat flux distribution over a 3D engineering configuration,i.e.a Hermes-like space shuttle model.The obtained numerical results are compared with experimental data.The predicted results demonstrate that the coupled multi-dimensional approach has a good prediction capability on aerodynamic heating over a wide range of complex engineering configurations.展开更多
Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind sch...Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.展开更多
The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. T...The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.展开更多
Targeting the problem of large amounts of gas emission from the goaf of the No.14201 working face in the Shaqu coal mine of Huajin Coking Coal Co. Ltd., we used a negative exponential function to describe the attenuat...Targeting the problem of large amounts of gas emission from the goaf of the No.14201 working face in the Shaqu coal mine of Huajin Coking Coal Co. Ltd., we used a negative exponential function to describe the attenuation process of gas emission in goaf (the stable source) based on the principle of field flow. Equations of two-component flow (gas and air) and seep- age-diffusion in a heterogeneous goaf flow field are solved by means of numerical simulation and fluid mechanics principles of air movement and gas distribution during gas emission from goaf. The results indicate that the air diversion volume has a negative, exponential relation with the volume of gas emitted from goaf to the working face and is clearly inversely related to gas concentra- tion. We calculated the minimum amount of air diversion and distributed air volume in the tailing roadway required for safe pro- duction.展开更多
文摘This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employed in conjunction with either the Jacobi or the Gauss-Seidel iteration process, one can obtain computed solutions that are accurate and free of unphysical
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘In this paper,we develop a fourth-order conservative wavelet-based shock-capturing scheme.The scheme is constructed by combining a wavelet collocation upwind method with the monotonic tangent of hyperbola for interface capturing(THINC)technique.We employ boundary variation diminishing(BVD)reconstruction to enhance the scheme’s effectiveness in handling shocks.First,we prove that wavelet collocation upwind schemes based on interpolating wavelets can be reformulated into a conservative form within the framework of wavelet theory,forming the foundation of the proposed scheme.The new fourthorder accurate scheme possesses significantly better spectral resolution than the fifth-and even seventh-order WENO-Z(weighted essentially non-oscillatory)schemes over the entire wave-number range.Moreover,the inherent low-pass filtering property of the wavelet bases allows them to filter high-frequency numerical oscillations,endowing the wavelet upwind scheme with robustness and accuracy in solving problems under extreme conditions.Notably,due to the wavelet multiresolution approximation,the proposed scheme possesses a distinctive shape-preserving property absent in the WENO-Z schemes and the fifth-order schemes with BVD reconstruction based on polynomials.Furthermore,compared to the fifth-order scheme with BVD reconstruction based on polynomials—which is significantly superior to the WENO schemes—the proposed scheme further enhances the ability to capture discontinuities.
文摘In this paper,we present a new fourth-order upwinding embedded boundary method(UEBM)over Cartesian grids,originally proposed in the Journal of Computational Physics[190(2003),pp.159-183.]as a second-order method for treating material interfaces for Maxwell’s equations.In addition to the idea of the UEBM to evolve solutions at interfaces,we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces.As a result,Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method,in contrast to the original second-order UEBM based on a Lax-Wendroff type difference.The final scheme allows time step sizes independent of the interface locations.Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method.We tested the scheme for several wave problems with various material interface locations,including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis.
基金supported by the Natural Science Foundation of Shandong Province(ZR2021MA019)the National Natural Science Foundation of China(11871312)。
文摘In this paper,a composite numerical scheme is proposed to solve the threedimensional Darcy-Forchheimer miscible displacement problem with positive semi-definite assumptions.A mixed finite element is used for the fow equation.The velocity and pressure are computed simultaneously.The accuracy of velocity is improved one order.The concentration equation is solved by using mixed finite element,multi-step difference and upwind approximation.A multi-step method is used to approximate time derivative for improving the accuracy.The upwind approximation and an expanded mixed finite element are adopted to solve the convection and diffusion,respectively.The composite method could compute the diffusion flux and its gradient.It possibly becomes an eficient tool for solving convection-dominated diffusion problems.Firstly,the conservation of mass holds.Secondly,the multi-step method has high accuracy.Thirdly,the upwind approximation could avoid numerical dispersion.Using numerical analysis of a priori estimates and special techniques of differential equations,we give an error estimates for a positive definite problem.Numerical experiments illustrate its computational efficiency and feasibility of application.
文摘It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.
基金Supported by the Aeronautical Science Foundation of China(2008ZC52039)~~
文摘The computational fluid dynamics （CFD） method is used to investigate the aerodynamic characteristics of the seat/occupant with windblast protection devices. The upwind Osher scheme is used for the spatial discretisation. The detached-eddy simulation （DES） based on the Spalart-Allmaras one-equation turbulence model is ap- plied to the detached viscous flow simulation behind the seat/occupant, with Mach numbers 0.6 and 1.2 at attack angles between --10 and 30°, and at two sideslip angles of 0 and 15°, respectively. The aerodynamic characteristics of seat/occupants with and without windblast protection devices are calculated in cases of the freestream Mach numbers 0. 8 and 1.6, attack angles from 5 to 30°, and three sideslip angles of 0, --20 and --50°, respectively. Results show that simulation results agree well with experimental data. And the occupant is efficiently protected by windblast protection devices.
文摘Adaptive Delaunay triangulation is combined with the cell-centered upwinding algorithm to analyze inviscid high-speed compressible flow problems. The multidimensional dissipation scheme was developed and included in the upwinding algorithm for unstructured triangular meshes to improve the computed shock wave resolution. The solution accuracy is further improved by coupling an error estimation procedure to a remeshing algorithm that generates small elements in regions with large change of solution gradients, and at the same time, larger elements in other regions. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. Efficiency of the combined procedure is evaluated by analyzing supersonic shocks and shock propagation behaviors for both the steady and unsteady high-speed compressible flows.
文摘A parallelized upwind flux splitting scheme for supersonic reacting flows on hybrid meshes is presented. The complexity of super/hyper-sonic combustion flows makes it necessary to establish solvers with higher resolution and efficiency for multi-component Euler/N-S equations. Hence, a spatial second-order van Leer type flux vector splitting scheme is established by introducing auxiliary points in interpolation, and a domain decomposition method used on unstructured hybrid meshes for obtaining high calculating efficiency. The numerical scheme with five-stage Runge-Kutta time step method is implemented to the simulation of combustion flows, including the supersonic hydrogen/air combustion and the normal injection of hydrogen into reacting flows. Satisfying results are obtained compared with limited references.
基金co-supported by the National Natural Science Foundation of China (Nos. 11272150, 10872094 and 10602024)
文摘A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes（RANS） equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method＂ and ‘‘minimum distance scheme of donor elements method＂ are established in this work. To improve the computational efficiency, Message Passing Interface（MPI） parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage（FAS） multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.
基金Project supported by the National Natural Science Foundation of China （Nos. 51005209 and 51375449）
文摘To improve lubrication effect and seal performance, complicated geometrical hydrodynamic grooves or patterns are often processed on end faces of liquid lubricated mechanical seals. These structures can lead to difficulties in precisely estimating the seal performance. In this study, an efficient adaptive finite element method （FEM） algorithm with mass conservation was presented, in which a streamline upwind/Petrov-Galerkin （SUPG） weighted residual FEM and a fast iteration algorithm were applied to solve the lubrication equations （Reynolds equation）. A mesh adaptation technique was utilized to refine the computation domain based on a residual posterior error estimator. Validation, applicability, and efficiency were verified by comparison among different algorithms and by case studies on seals＇ faces with different groove structures. The study investigated the influence of the order of shape function and the mesh number on the leakage balance. Mesh refinement occurred mainly in cavitation zones when cavitation happened, otherwise it occurred in regions with a high pressure gradient. Numerical experiments verified that the proposed algorithm is a fast, effective, and accurate method to simulate lubrication problems in the engineering field apart from end face seals.
基金supported by National Natural Science Foundation of China(11101244,11271231)National Tackling Key Problems Program(20050200069)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
基金NKBRSF CG 1990 3 2 80 5 National Natural Science F oundation of China !( No.5 98760 0 2 )
文摘In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.
文摘A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.
文摘The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence. The mathematical model of the problem and upwind splitting alternating direction method were presented. Using this method, the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Provivce was finished. The numerical results turned out to be identical with the real measurements, so the prediction of the consequences of protection projectects is reasonable.
基金the National Key Research&Development Program of China(2016YFB020071)the National Natural Science Foundation of China(Grants 11532016 and 11702315).
文摘The simulation of hypersonic flows with fully unstructured(tetrahedral)grids has severe problems with respect to the prediction of stagnation region heating,due to the random face orientation without alignment to the bow shock.To improve the accuracy of aero-heating predictions,three multi-dimensional approaches on unstructured grids are coupled in our Reynolds-averaged Navier-Stokes(RANS)solver,including multi-dimensional upwind flux reconstruction(MUP),multi-dimensional limiter(MLP-u2)and multi-dimensional gradient reconstruction(MLR).The coupled multi-dimensional RANS solver is validated by several typical verification and validation(V&V)cases,including hypersonic flows over a cylinder,a blunt biconic,and a double-ellipsoid,with commonly used prism/tetrahedral hybrid grids.Finally,the coupled multi-dimensional solver is applied to simulating the heat flux distribution over a 3D engineering configuration,i.e.a Hermes-like space shuttle model.The obtained numerical results are compared with experimental data.The predicted results demonstrate that the coupled multi-dimensional approach has a good prediction capability on aerodynamic heating over a wide range of complex engineering configurations.
基金supported by the Department of Science & Technology, Government of India under research grant SR/S4/MS:318/06.
文摘Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.
文摘The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.
基金Project 50574038 supported by the National Natural Science Foundation of China
文摘Targeting the problem of large amounts of gas emission from the goaf of the No.14201 working face in the Shaqu coal mine of Huajin Coking Coal Co. Ltd., we used a negative exponential function to describe the attenuation process of gas emission in goaf (the stable source) based on the principle of field flow. Equations of two-component flow (gas and air) and seep- age-diffusion in a heterogeneous goaf flow field are solved by means of numerical simulation and fluid mechanics principles of air movement and gas distribution during gas emission from goaf. The results indicate that the air diversion volume has a negative, exponential relation with the volume of gas emitted from goaf to the working face and is clearly inversely related to gas concentra- tion. We calculated the minimum amount of air diversion and distributed air volume in the tailing roadway required for safe pro- duction.
