The Research And Application Of Meshless Method For CFD With Some Key Technologies

Grid cells are the basis of the traditional numerical methods (finite difference methods, finite volume methods, finite element methods) in computational fluid dynamics (CFD). The simulation results are depended on the quality of the grid mostly. High quality grid generation is a tedious and challenge work when dealing with three dimensional complecated geometries. Establishing an accurate and efficient grid based method to simulate multi-body separation or interaction problems is very difficult. Gridless method which doesn’t need the information of the grid, solves the governing equations by the local cloud of points in the computational domain. The gridless method is more advanced than the traditional methods when dealing with the complecated geometries, moving boundary flow problems. This dissertation, supported by the National Natural Science Foundation of China, describes the developments and the applications of some key technologies about gridless method by the means of programming.Firstly, the gridless algorithm which can solve steady, unsteady flows on all Mach numbers is developed based on Euler equations. For this gridless algorithm, the least-squares method is used to fit the special derivatives, the upwind AUSM-family schemes are introduced to calculate the flux at the middle ghost point, the MUSCL scheme is adopted to improve the accuracy, and the Van Albada limiter is used to prevent the non-physical oscillation near the discontinuity and the shock, the SSP Runge-Kutta method is applied to the time integration. To validate the accuracy and the robustness of the gridless method, Sod shock tube problem, shock impingement on single cylinder, Emery problem, inviscid flow around NACA0012 airfoil are simulated with gridless method presented. The numerical results are compared with the analytical solution, experimental data or the other numerical results obtained by traditional methods.Secondly, the gridless method solving viscous flows based on Navier-Stokes equations is investigated. It is found that, when using the least-squares method to solve the N-S equations directly, high anisotropic structure of cloud of points is always exited resulting in ill-conditioned least squares coefficient matrix. It becomes very difficult for any mathematical method to obtain the accurate spatial derivatives. The concept named cloud of points reconstruction is proposed aimed at such situation. With this technology, the high anisotropic structure of cloud points can be transformed into nearly isotropic structure in certain local regions like the near wall and weak regions, the robust and stable coefficient matrix can be formed, and the accurate spatial derivatives can be obtained. On the basis of this technology, the least squares gridless method is applied to turbulence flow simulations by coupling the RANS two equation turbulence models (k-co SST model and k-co TNT model) and the N-S equations further. The predictive ability are compared and analyzed by simulating turbulence flows in varying separated degrees. The successful implementation provides a certain reference to selection of turbulence models within the gridless framework.Thirdly, the hybrid gridless/Cartesian grid approach is proposed in consideration of low efficiency of gridless method. The hybrid approach uses a Cartesian grid to cover most of the computational domain and a gridless method to calculate a relatively small region adjacent to the body surface, making use of the flexibility of the gridless method in handling surface with complicated geometry and the computational efficiency of the Cartesian grid. Within the overlapping region, some key technologies like "hole cutting", node identification, interpolation method are used to couple the two solvers. Some cases are conducted to examine the ability, accuracy, robustness of this hybrid approach. The computational results show that the hybrid method can capture the shape and the location of shock accurately, and can be applied to simulating 3D complicated geometry (B1AC2R generic missile).Lastly, the gridless/Cartesian grid approach is applied to moving boundary flow problems as a result of the accuracy and efficiency in simulating steady flows. By implementing a dynamic hole cutting, node identification and information communication in the overlapping region, unsteady flow over a pitching NACA0012 airfoil is performed, the computational results show a good agreement with the earlier experimental data as well as some other computational results. The simulation of the sub calibre APFSDS launch, muzzle and the separation of the projectile and the sabots, is also performed by coupling the Arbitrary-Lagrangian Eulerian (ALE) equations and the motion equations of six-DOF (degree of freedom). It shows that the dynamic hybrid gridless/Cartesian grid approach has the flexible processing capability to dealing with the practical complex multi-body separation, and the work presented also provides a new research way for the design and test of APFSDS.