The artificial compression method (ACM) that is generally used to capture the contact discontinuity in nonviscous flows is used here in the simulation of quasi-geostrophic ideal frontogenesis in two dimensions. A comp...The artificial compression method (ACM) that is generally used to capture the contact discontinuity in nonviscous flows is used here in the simulation of quasi-geostrophic ideal frontogenesis in two dimensions. A comparison is made among the result of the ACM, the simulation result of Cullen, and the exact solution of the semi-geostrophic equations. The simulated front in this paper is more prominent than Cullen′s and is much closer to the exact solution.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 numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using th...The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.展开更多
This paper is a continuation of the domain decomposition method according to thephysics scale proposed in [1] and [2]. Starting from systems of ordinary differentialequattons, a solution is decomposed into an outer so...This paper is a continuation of the domain decomposition method according to thephysics scale proposed in [1] and [2]. Starting from systems of ordinary differentialequattons, a solution is decomposed into an outer solution (0) and its boundary layercorrections (BLC) mainly on the fixed boundary. For efficient numerical solution,different equations, different numerical methods and different grids can be suitablychosen for the different scales. This paper also gives the characteristic nature and well-posed boundary condition about artificial compressible equations. Numericalexperiments show that the computational method and the couple process presented inthe paper are effective.展开更多
The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unste...The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×10^4.Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.展开更多
A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broad...A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.展开更多
This research studies the changes in flow patterns and hemodynamic parameters of diverse shapes and sizes of stenosis.Six different shapes and sizes of stenosis are constructed to investigate the variations in hemodyn...This research studies the changes in flow patterns and hemodynamic parameters of diverse shapes and sizes of stenosis.Six different shapes and sizes of stenosis are constructed to investigate the variations in hemodynamics as the morphology changes.Changes in shape(trapezoidal and bell-shaped)and sizes of stenosis change the stresses on the walls and their flow patterns.TAWSS and OSI results specify that trapezoidal stenosis exerts greater stress than bell-shaped stenosis.Also,as the length of the trapezoidal stenosis increases,the TAWSS increases,whereas the trend is the opposite for bell-shaped stenosis.Later,this paper also studies different degrees of stenosis extracted from real images.Changes in velocity flow patterns,wall shear stress(WSS),Time-averaged wall shear stress(TAWSS)and Oscillatory shear index(OSI)have been studied for these images.Results illustrate that the peak velocity rises drastically as the stenosis percentage increases.Negative velocity is seen close to the artery's walls,indicating flow separation.This flow separation region is seen throughout the cycle except in the accelerating flow region.An increase in stenosis also increases WSS and TAWSS drastically.Negative WSS is seen downstream of stenosis,indicating flow recirculation.Such negative WSS in the blood vessels also promotes endothelial dysfunction.OSI values greater than 0.2 are seen near the stenosis region,indicating atherosclerosis growth.Regions of high OSI and low TAWSS are also identified,indicating probable regions of plaque development.展开更多
This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is...This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied.The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact scheme.The solution algorithm used is the Beam-Warming approximate factorization scheme.Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are presented.The computed results are found in good agreement with established analytical and numerical results.The third-order accuracy of the scheme is verified on uniform rectangular meshes.展开更多
In this work,we develop a novel high-order discontinuous Galerkin(DG)method for solving the incompressible Navier-Stokes equations with variable density.The incompressibility constraint at cell interfaces is relaxed b...In this work,we develop a novel high-order discontinuous Galerkin(DG)method for solving the incompressible Navier-Stokes equations with variable density.The incompressibility constraint at cell interfaces is relaxed by an artificial compressibility term.Then,since the hyperbolic nature of the governing equations is recovered,the simple and robust Harten-Lax-van Leer(HLL)flux is applied to discrete the inviscid term of the variable density incompressible Navier-Stokes equations.The viscous term is discretized by the direct DG(DDG)method,the construction of which was initially inspired by the weak solution of a scalar diffusion equation.In addition,in order to eliminate the spurious oscillations around sharp density gradients,a local slope limiting operator is also applied during the highly stratified flow simulations.The convergence property and performance of the present high-order DDG method are well demonstrated by several benchmark and challenging numerical test cases.Due to its advantages of simplicity and robustness in implementation,the present method offers an effective approach for simulating the variable density incompressible flows.展开更多
This paper presents a comprehensive overview of the element-wise locally conservative Galerkin(LCG)method.The LCG method was developed to find a method that had the advantages of the discontinuous Galerkin methods,wit...This paper presents a comprehensive overview of the element-wise locally conservative Galerkin(LCG)method.The LCG method was developed to find a method that had the advantages of the discontinuous Galerkin methods,without the large computational and memory requirements.The initial application of the method is discussed,to the simple scalar transient convection-diffusion equation,along with its extension to the Navier-Stokes equations utilising the Characteristic Based Split(CBS)scheme.The element-by-element solution approach removes the standard finite element assembly necessity,with an face flux providing continuity between these elemental subdomains.This face flux provides explicit local conservation and can be determined via a simple small post-processing calculation.The LCG method obtains a unique solution from the elemental contributions through the use of simple averaging.It is shown within this paper that the LCG method provides equivalent solutions to the continuous(global)Galerkin method for both steady state and transient solutions.Several numerical examples are provided to demonstrate the abilities of the LCG method.展开更多
基金The project was supported by the Nutional Key Planning Development Project for Basic Research (G199903280l)the Key Innovition Project of the Chinese Academy of Sciences (KZCX2-208).
文摘The artificial compression method (ACM) that is generally used to capture the contact discontinuity in nonviscous flows is used here in the simulation of quasi-geostrophic ideal frontogenesis in two dimensions. A comparison is made among the result of the ACM, the simulation result of Cullen, and the exact solution of the semi-geostrophic equations. The simulated front in this paper is more prominent than Cullen′s and is much closer to the exact solution.
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.
基金The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the Large Groups Project under grant number RGP.2/235/43.
文摘The numerical solution of compressible flows has become more prevalent than that of incompressible flows.With the help of the artificial compressibility approach,incompressible flows can be solved numerically using the same methods as compressible ones.The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations.Any numerical method highly depends on its accuracy and speed of convergence.Although the artificial compressibility approach is utilized in several numerical simulations,the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies.Therefore,this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow.To improve the stability and convergence speed of time discretizations,the fifth-order Runge-Kutta method is applied.A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids.The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation.The optimum artificial compressibility is found to be between 1 and 5.These findings can be utilized to enhance the performance of commercial numerical simulation tools,including ANSYS and COMSOL.
文摘This paper is a continuation of the domain decomposition method according to thephysics scale proposed in [1] and [2]. Starting from systems of ordinary differentialequattons, a solution is decomposed into an outer solution (0) and its boundary layercorrections (BLC) mainly on the fixed boundary. For efficient numerical solution,different equations, different numerical methods and different grids can be suitablychosen for the different scales. This paper also gives the characteristic nature and well-posed boundary condition about artificial compressible equations. Numericalexperiments show that the computational method and the couple process presented inthe paper are effective.
基金Supported by the Technology Innovation Program(Grant number:10053121)funded by the Ministry of Trade,Industry&Energy(MI,Korea)by the Energy Efficiency&Resource of Korea Institute of Energy Technology Evaluation and Planning(KETEP)grant funded by the Ministry of Knowledge Economy of Korea(Grant number:2014301002-1870)
文摘The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×10^4.Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.
基金supported by the National Natural Science Foundation of China(Grant No.11402016)the Fundamental Research Funds for the Central Universities(Grant Nos.50100002014105020&50100002015105033)
文摘A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.
文摘This research studies the changes in flow patterns and hemodynamic parameters of diverse shapes and sizes of stenosis.Six different shapes and sizes of stenosis are constructed to investigate the variations in hemodynamics as the morphology changes.Changes in shape(trapezoidal and bell-shaped)and sizes of stenosis change the stresses on the walls and their flow patterns.TAWSS and OSI results specify that trapezoidal stenosis exerts greater stress than bell-shaped stenosis.Also,as the length of the trapezoidal stenosis increases,the TAWSS increases,whereas the trend is the opposite for bell-shaped stenosis.Later,this paper also studies different degrees of stenosis extracted from real images.Changes in velocity flow patterns,wall shear stress(WSS),Time-averaged wall shear stress(TAWSS)and Oscillatory shear index(OSI)have been studied for these images.Results illustrate that the peak velocity rises drastically as the stenosis percentage increases.Negative velocity is seen close to the artery's walls,indicating flow separation.This flow separation region is seen throughout the cycle except in the accelerating flow region.An increase in stenosis also increases WSS and TAWSS drastically.Negative WSS is seen downstream of stenosis,indicating flow recirculation.Such negative WSS in the blood vessels also promotes endothelial dysfunction.OSI values greater than 0.2 are seen near the stenosis region,indicating atherosclerosis growth.Regions of high OSI and low TAWSS are also identified,indicating probable regions of plaque development.
基金This work was supported by Natural Science Foundation of China(G10476032,G10531080)state key program for developing basic sciences(2005CB321703).
文摘This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied.The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact scheme.The solution algorithm used is the Beam-Warming approximate factorization scheme.Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are presented.The computed results are found in good agreement with established analytical and numerical results.The third-order accuracy of the scheme is verified on uniform rectangular meshes.
基金supported by theNationalNatural Science Foundation of China No.12001020.
文摘In this work,we develop a novel high-order discontinuous Galerkin(DG)method for solving the incompressible Navier-Stokes equations with variable density.The incompressibility constraint at cell interfaces is relaxed by an artificial compressibility term.Then,since the hyperbolic nature of the governing equations is recovered,the simple and robust Harten-Lax-van Leer(HLL)flux is applied to discrete the inviscid term of the variable density incompressible Navier-Stokes equations.The viscous term is discretized by the direct DG(DDG)method,the construction of which was initially inspired by the weak solution of a scalar diffusion equation.In addition,in order to eliminate the spurious oscillations around sharp density gradients,a local slope limiting operator is also applied during the highly stratified flow simulations.The convergence property and performance of the present high-order DDG method are well demonstrated by several benchmark and challenging numerical test cases.Due to its advantages of simplicity and robustness in implementation,the present method offers an effective approach for simulating the variable density incompressible flows.
文摘This paper presents a comprehensive overview of the element-wise locally conservative Galerkin(LCG)method.The LCG method was developed to find a method that had the advantages of the discontinuous Galerkin methods,without the large computational and memory requirements.The initial application of the method is discussed,to the simple scalar transient convection-diffusion equation,along with its extension to the Navier-Stokes equations utilising the Characteristic Based Split(CBS)scheme.The element-by-element solution approach removes the standard finite element assembly necessity,with an face flux providing continuity between these elemental subdomains.This face flux provides explicit local conservation and can be determined via a simple small post-processing calculation.The LCG method obtains a unique solution from the elemental contributions through the use of simple averaging.It is shown within this paper that the LCG method provides equivalent solutions to the continuous(global)Galerkin method for both steady state and transient solutions.Several numerical examples are provided to demonstrate the abilities of the LCG method.
