Numerical Method Of Turbulent Flow Simulation Based On Gas-kinetic Scheme

The simulation of turbulent flows is one of the difficult problems in the field of the computational fluid dynamics(CFD).The development of turbulence simulation is dependent on the turbulence theory,the simulation method of turbulent flow and the numerical scheme.The numerical method is of great importance to the turbulence simulation.Compared with the numerical method based on the Navier-Stokes equation,the gas-kinetic scheme(GKS)is more comprehensive in the physical essence.GKS based on the BGK model can predict the flow field in the view of mesoscopic method.Turbulent flow is the typical multi-scale fluid flow and the turbulence simulation can be benefited from the multi-scale property of GKS.The simulation of turbulent flow requires the numerical method can resolve the flow field with enough resolution,which leads to very large grid size and expensive computational costs.Using hybrid grid and time accelerating method can reduce the computational cost and improve the computational efficiency greatly.Compared with the lower-order numerical method,the high-order method can resolve the flow field quite well.In present work,the dual time-stepping method for GKS and high-order gas-kinetic scheme are developed,and the numerical simulation of turbulent flow is carried out using the developed method.The main work and innovation points of this thesis are as follow1.To predict the turbulent flows more efficiently,the dual time-stepping stragegy for GKS is developed.The idea is borrowed from the traditional numerical method based on the Navier-Stokes equation.To approach the pseudo-steady state,the Reverse-Cuthill-McKee(RCM)method,incomplete lower-upper factorization scheme(ILU)preconditioner and generalized minimal residual algorithm(GMRES)are applied to solve the linear system efficiently.In the simulation of incompressible flow around circular cylinder,the transonic NACA0012 airfoil buffet and the turbulent flow around a square cylinder,the accuracy of dual timestepping method and the availability of the numerical code have been verified.Compared with explicit scheme,the dual time-stepping method can improve the computational efficiency of turbulent flow simulation more than 10 times.2.The GKS coupled turbulence model method is extended to simulate the large Reynolds number flow,and the parallel code is developed.In the field of aerospace engineering,the Reynolds number is always up to millions.To develop the GKS coupled turbulence model method is of great importance in the simulation of large Reynolds number flow.In present work,the SA/SST turbulence model are coupled with GKS,and the numerical computation code is also developed.The turbulent flow over a flat plate,the transonic flow around the RAE2822 airfoil are simulated to validated the behavior of present algorithm and code.The transonic flow around ONERA M6 wing is simulated and the potential of coupled method to approach the complex turbulent flow is evident.3.The compact high-order gas-kientic schemes are developed for high resolution requirement of turbulence simulation.Depending on the compact least-squares(CLS)method and third order gas-kinetic flux solver,the present method can reach to designed accuracy order on structured and unstructured grid within a single stage.To reduce the cost of flux computation and improve the efficiency of simulation,FRKIF is developed based on the flux reconstruction(FR)method and kinetic inviscid flux(KIF)solver.Using central scheme to solve the viscous flux,FRKIF can keep the advantages of gas-kinetic scheme and be easily integrated into the existing CFD code.4.The large-eddy simulation method is developed based on the FRKIF method,and the parellel code is also developed.Several sub-grid scale models and wall models are available in the large-eddy simulation.The effect of compressibility of FRKIF to incompressible turbulent flow is examined.The accuracy order of numerical method has a great effect to the resolution of numerical results which is verified using the case of Taylor-Green vortex flow.The behavior of filter,subgrid model and wall model are also examined in the simulation of Taylor-Green vortex flow using the large-eddy simulation method.The success simulation of Taylor-Green vortex flow,turbulent cavity flow and the subcritical flow around the circular cylinder have proved the accuracy and ability of present method in the simulation of turbulent flows.