Investigations Of Convergence Acceleration And Complex Flow Numerical Simulation For High-Order Accurate Scheme (WCNS)

As a class of numerical tools, high-order accurate scheme has been playing an important role in many calculation domains of science and technology, such as direct numerical simulation (DNS) and large eddy simulation (LES) for turbulence flows, computational AeroAcoustics (CAA), computational electro-magnetics (CEM) and magneto-hydrodynamic (MHD). Computations with high-order scheme can provide flow data and details for observations and analyses, and can make up for the limitations of wind-tunnel experiments and drawbacks of theories. Especially, with the increasing requirements for the accuracy of computations, more and more refined and exact numerical simulations are needed in application and research fields. In this context, high-order weighted compact nonlinear scheme (WCNS) is studied and applied further in this dissertation, and some valuable conclusions and computational experiences are obtained.The purpose of this thesis is to develop and exploit WCNS's potential in practical computations, investigate its numerical characters in simulations of complex flows, and extend its application scope. Additionally, it is expected to improve understanding of some flow mechanisms, and bestead the future works about high-order accuracy computations.This thesis contains six chapters as follows:Chapter one is the introduction, in which the state of arts of high-order accurate scheme in computational fluid dynamics (CFD) are reviewed. This section presents the evolution and properties of WCNS and points out the handicap in applications. Also, this chapter narrates the meaning of WCNS for using in the complex flows of turbulence and boundary-layer receptivity. Finally, the current research works are described in brief.Chapter two presents the numerical methods used in this dissertation. The main contents include: governing equations, space discretization, time integration, boundary conditions, turbulence models and aerodynamic coefficient formulas.In chapter three, a number of different implicit time methods are compared with each other for several supersonic flows over cylinder and sphere, when the high-order scheme of WCNS-E-5 is used in the discretization of space terms. The time methods involve LU-SGS, Gauss-Seidel point relaxation and line relaxation, and generalized minimum residual (GMRES) algorithm. To evaluate convergence of time methods, the influences of many factors including time step, sub-iteration number and precondition method of GMRES, are considered in the numerical experiments. The results show that the using of accurate analytical Jacobians in the left hand of discretized equations can improve the convergence of WCNS-E-5, and the GMRES method can accelerate the converging process further. And, these methods are successfully employed in more complex hypersonic flows over double-ellipse.In chapter four, the discrepancies in turbulence simulation between five-order accurate scheme WCNS-E-5 and two-order accurate scheme MUSCL are researched in the numerical cases of transonic flows over RAE2822 airfoil and M6 wing and low-speed high-attack-angle separation flows over slender cylinder. The effects induced from grids, inviscous flux formulas and turbulence models are carefully investigated with comparisons. The preliminary results indicate that the dissipation error level of numerical scheme has remarkable influence on the simulations of turbulent flows, and that the computation of high-order scheme WCNS is affected little by the factors except for turbulence models. Therefore, high-order scheme can obtain more reliable and accurate turbulence solutions and do more benefits for turbulence modeling.In chapter five, WCNS-E-5 is applied to directly simulating the receptivity processes of hypersonic boundary-layer to acoustic disturbance. The receptivity case of parabola leading-edge is adopted to validate the spatial resolution of WCNS-E-5. The temporal resolution and efficiency of single-time-step implicit scheme are also studied in contrast with Runge-Kutta explicit time scheme. It is found that the space and time methods employed in this thesis are accurate enough and highly efficient. Using these methods, a series of receptivity simulations for flat plate boundary-layer to two-dimension acoustic wave are systemically carried out with consideration of many parameter effects involving wall cooling, fast/slow wave, incidence angle and leading-edge thickness. From these massive calculations, the understanding of physical process is improved and some meaningful conclusions are achieved for receptivity researches.Chapter six reviews all works in this dissertation and gives the concluding remarks and the future research directions.Finally, the references and acknowledgements are presented.