Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
To apply the fictitious domain method and conduct numericalexperiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different valuesof the it...To apply the fictitious domain method and conduct numericalexperiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different valuesof the iterative parameter τ and the small parameter ε are presented. Astudy of the auxiliary problem of the fictitious domain method for NavierStokes equations with continuation into a fictitious subdomain by highercoefficients with a small parameter is carried out. A generalized solutionof the auxiliary problem of the fictitious domain method with continuationby higher coefficients with a small parameter is determined. After all theabove mathematical studies, a computational algorithm has been developedfor the numerical solution of the problem. Two methods were used to solvethe problem numerically. The first variant is the fictitious domain methodassociated with the modification of nonlinear terms in a fictitious subdomain.The model problem shows the effectiveness of using such a modification. Theproposed version of the method is used to solve two problems at once that arisewhile numerically solving systems of Navier-Stokes equations: the problem ofa curved boundary of an arbitrary domain and the problem of absence of aboundary condition for pressure in physical formulation of the internal flowproblem. The main advantage of this method is its universality in developmentof computer programs. The second method used calculation on a uniform gridinside the area. When numerically implementing the solution on a uniformgrid inside the domain, using this method it’s possible to accurately take intoaccount the boundaries of the curved domain and ensure the accuracy of thevalue of the function at the boundaries of the domain. Methodical calculationswere carried out, the results of numerical calculations were obtained. Whenconducting numerical experiments in both cases, quantitative and qualitativeindicators of numerical results coincide.展开更多
In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can giv...In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can give convergent results for viscous flows with high Reynolds number. As an example, the results of shear-driven cavity flow with high Reynolds number up to 25000 on fine grid 257×257 are given.展开更多
To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and invest...To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Rtmge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.展开更多
Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iterat...Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iteration for the equations on a coarse grid,where a Stokes problem is solved at each iteration.Then,on overlapped local fine grids,corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution.Error bounds of the approximate solution are derived.Numerical results on examples of known analytical solutions,lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.展开更多
The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation...The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided.展开更多
In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed...In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.展开更多
The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of ...The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel （LU-SGS） method in the streamwise direction in a space marching manner. The AUSMPW＋ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu＇s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.展开更多
Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of un...Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.展开更多
This paper aims to investigate a dam break in a channel with a bend in the presence of several obstacles.To accurately determine the flood zones,it is necessary to take into account many factors such as terrain,reserv...This paper aims to investigate a dam break in a channel with a bend in the presence of several obstacles.To accurately determine the flood zones,it is necessary to take into account many factors such as terrain,reservoir volume.Numerical modeling was used to determine the flood zone.Numerical modeling based on the Navier-Stokes equations with a turbulent k-epsilon RNG model,the Volume of Fluid(VOF)method and the PISO algorithm were used to analyze the flow in a bend channel at an angle of 10 with the obstacles.To verify the numerical model,a test on dam break in the 450 channel was conducted.The simulation results were compared with experimental data and with the numerical data of existing data.Having been convinced of the correctness of the mathematical model,the authors carried out a numerical simulation of the main problem in three versions:without barriers,with one obstacle,with two obstacles.According to the obtained numerical results,it can be noted that irregular landforms held the flow,a decrease in water level and a slower time for water emergence could be seen.Thus,the water flow without an obstacle,with one obstacle and with two obstacles showed 4.2 s,4.4 s and 4.6 s of the time of water appearance,respectively.This time shift can give a certain advantage when conducting various events to evacuate people.展开更多
The misoperation of hydraulic components such as pumps and valves in pressurized pipelines triggers water hammer phenomena and seriously threats the safe operation of hydraulic systems.At present,the main water hammer...The misoperation of hydraulic components such as pumps and valves in pressurized pipelines triggers water hammer phenomena and seriously threats the safe operation of hydraulic systems.At present,the main water hammer simulation methods are method of characteristics(MOC),and further investigation of new algorithms is needed.Therefore,a new method for simulating the water hammer using the finite volume method(FVM),semi-implicit method for pressure linked equations(SIMPLE)algorithm is proposed in the present work.Compared with the experimental data,the accuracy and reliability of the proposed algorithm are verified.Results show that the IAB,MIAB friction models not only predict the first pressure peak but also accurately predict the pressure attenuation.From the comparison of the MOC,SIMPLE algorithms,the results of the two algorithms are almost the same in front of the valve,while near the upstream tank,when using the same friction model,the pressure attenuation predicted by the SIMPLE algorithm is slightly greater than that of the MOC method and closer to the experimental data.Therefore,the newly proposed algorithm can serve as an alternative to the MOC method in simulating water hammer.The investigation enriches the numerical methods of hydraulic transients and lays the foundation for subsequent program development.展开更多
This paper covers the dynamics problems. The review and some aspects of main development stages of using Multigrid method for fluid multigrid technics are presented. Some approaches for solving Navier-Stokes equations...This paper covers the dynamics problems. The review and some aspects of main development stages of using Multigrid method for fluid multigrid technics are presented. Some approaches for solving Navier-Stokes equations and convection- diffusion problems are considered.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan(Grant No.AP09058430)。
文摘To apply the fictitious domain method and conduct numericalexperiments, a boundary value problem for an ordinary differential equation is considered. The results of numerical calculations for different valuesof the iterative parameter τ and the small parameter ε are presented. Astudy of the auxiliary problem of the fictitious domain method for NavierStokes equations with continuation into a fictitious subdomain by highercoefficients with a small parameter is carried out. A generalized solutionof the auxiliary problem of the fictitious domain method with continuationby higher coefficients with a small parameter is determined. After all theabove mathematical studies, a computational algorithm has been developedfor the numerical solution of the problem. Two methods were used to solvethe problem numerically. The first variant is the fictitious domain methodassociated with the modification of nonlinear terms in a fictitious subdomain.The model problem shows the effectiveness of using such a modification. Theproposed version of the method is used to solve two problems at once that arisewhile numerically solving systems of Navier-Stokes equations: the problem ofa curved boundary of an arbitrary domain and the problem of absence of aboundary condition for pressure in physical formulation of the internal flowproblem. The main advantage of this method is its universality in developmentof computer programs. The second method used calculation on a uniform gridinside the area. When numerically implementing the solution on a uniformgrid inside the domain, using this method it’s possible to accurately take intoaccount the boundaries of the curved domain and ensure the accuracy of thevalue of the function at the boundaries of the domain. Methodical calculationswere carried out, the results of numerical calculations were obtained. Whenconducting numerical experiments in both cases, quantitative and qualitativeindicators of numerical results coincide.
文摘In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can give convergent results for viscous flows with high Reynolds number. As an example, the results of shear-driven cavity flow with high Reynolds number up to 25000 on fine grid 257×257 are given.
文摘To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Rtmge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.
基金supported by the Natural Science Foundation of China(No.11361016)the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金the Scientific Research Foundation of Southwest University,Fundamental Research Funds for the Central Universities(No.XDJK2014C160,SWU113095)the Science and Technology Foundation of Guizhou Province,China(No.[2013]2212).
文摘Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iteration for the equations on a coarse grid,where a Stokes problem is solved at each iteration.Then,on overlapped local fine grids,corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution.Error bounds of the approximate solution are derived.Numerical results on examples of known analytical solutions,lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.
基金the National Nature Science Foundation of China (Grants No.50306019,No.10571142,No.10471110 and No.10471109)
文摘The stationary and nonstationary rotating Navier-Stokes equations with mixed boundary conditions are investigated in this paper. The existence and uniqueness of the solutions are obtained by the Galerkin approximation method. Next, θ-scheme of operator splitting algorithm is applied to rotating Navier-Stokes equations and two subproblems are derived. Finally, the computational algorithms for these subproblems are provided.
文摘In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.
基金supported by the National Natural Science Foundation of China (51176003)
文摘The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel （LU-SGS） method in the streamwise direction in a space marching manner. The AUSMPW＋ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu＇s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.
基金supported by the National Natural Science Foundation of China(No.92252201)the Fundamental Research Funds for the Central Universitiesthe Academic Excellence Foundation of Beihang University(BUAA)for PhD Students。
文摘Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.
基金supported by the grant from the Ministry of science and Higher education of the Republic of Kazakhstan(AP23489948).
文摘This paper aims to investigate a dam break in a channel with a bend in the presence of several obstacles.To accurately determine the flood zones,it is necessary to take into account many factors such as terrain,reservoir volume.Numerical modeling was used to determine the flood zone.Numerical modeling based on the Navier-Stokes equations with a turbulent k-epsilon RNG model,the Volume of Fluid(VOF)method and the PISO algorithm were used to analyze the flow in a bend channel at an angle of 10 with the obstacles.To verify the numerical model,a test on dam break in the 450 channel was conducted.The simulation results were compared with experimental data and with the numerical data of existing data.Having been convinced of the correctness of the mathematical model,the authors carried out a numerical simulation of the main problem in three versions:without barriers,with one obstacle,with two obstacles.According to the obtained numerical results,it can be noted that irregular landforms held the flow,a decrease in water level and a slower time for water emergence could be seen.Thus,the water flow without an obstacle,with one obstacle and with two obstacles showed 4.2 s,4.4 s and 4.6 s of the time of water appearance,respectively.This time shift can give a certain advantage when conducting various events to evacuate people.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52079140,52379095)。
文摘The misoperation of hydraulic components such as pumps and valves in pressurized pipelines triggers water hammer phenomena and seriously threats the safe operation of hydraulic systems.At present,the main water hammer simulation methods are method of characteristics(MOC),and further investigation of new algorithms is needed.Therefore,a new method for simulating the water hammer using the finite volume method(FVM),semi-implicit method for pressure linked equations(SIMPLE)algorithm is proposed in the present work.Compared with the experimental data,the accuracy and reliability of the proposed algorithm are verified.Results show that the IAB,MIAB friction models not only predict the first pressure peak but also accurately predict the pressure attenuation.From the comparison of the MOC,SIMPLE algorithms,the results of the two algorithms are almost the same in front of the valve,while near the upstream tank,when using the same friction model,the pressure attenuation predicted by the SIMPLE algorithm is slightly greater than that of the MOC method and closer to the experimental data.Therefore,the newly proposed algorithm can serve as an alternative to the MOC method in simulating water hammer.The investigation enriches the numerical methods of hydraulic transients and lays the foundation for subsequent program development.
文摘This paper covers the dynamics problems. The review and some aspects of main development stages of using Multigrid method for fluid multigrid technics are presented. Some approaches for solving Navier-Stokes equations and convection- diffusion problems are considered.
