Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still sub...Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.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
To simulate the incompressible turbulent flows,two models,known as the simplified and highly stable lattice Boltzmann method(SHSLBM)and large eddy simulation(LES)model,are employed in this paper.The SHSLBM was develop...To simulate the incompressible turbulent flows,two models,known as the simplified and highly stable lattice Boltzmann method(SHSLBM)and large eddy simulation(LES)model,are employed in this paper.The SHSLBM was developed for simulating incompressible viscous flows and showed great performance in numerical stability at high Reynolds numbers,which means that this model is capable of dealing with turbulent flows by adding the turbulence model.Therefore,the LES model is combined with SHSLBM.Inspired by the less amount of grids required for SHSLBM,a local grid refinement method is used at relatively high Reynolds numbers to improve computational efficiency.Several benchmark cases are simulated and the obtained numerical results are compared with the available results in literature,which show excellent agreement together with greater computational performance than other algorithms.展开更多
An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been ...An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.展开更多
By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improv...By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.展开更多
A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for-...A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.展开更多
基金supported by the National Natural Science Foundation of China(NSFC,Grant Numbers 10572106,10872153 and 11172219)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110013).
文摘Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.
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J.Wu acknowledges the support of the National Natural Science Foundation of China(Grant No.12072158)the Natural Science Foundation of Jiangsu Province(Grant No.BK20191271)+1 种基金the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(Grant No.MCMS-I-0120G02)This work is also supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘To simulate the incompressible turbulent flows,two models,known as the simplified and highly stable lattice Boltzmann method(SHSLBM)and large eddy simulation(LES)model,are employed in this paper.The SHSLBM was developed for simulating incompressible viscous flows and showed great performance in numerical stability at high Reynolds numbers,which means that this model is capable of dealing with turbulent flows by adding the turbulence model.Therefore,the LES model is combined with SHSLBM.Inspired by the less amount of grids required for SHSLBM,a local grid refinement method is used at relatively high Reynolds numbers to improve computational efficiency.Several benchmark cases are simulated and the obtained numerical results are compared with the available results in literature,which show excellent agreement together with greater computational performance than other algorithms.
文摘An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.
基金Project supported by the National Natural Science Foundation of China （Grant No 70271069）.
文摘By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.
基金the National Natural Science Foundation of China (Grants 41372301 and 51349011)the Preeminent Youth Talent Project of Southwest University of Science and Technology (Grant 13zx9109)
文摘A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.
