The Improvement And Its Extended Application Study Of Least-squares Meshless Method

With the rapid development of computer technology, high-performance parallel computing technology and computational fluid dynamics (CFD), numerical simulation is playing an important role in the research area of fluid dynamics. Due to the more and more complex geometry of aerocraft, there are some difficulties in the generation of structured or unstructured mesh. The unsteady flow including moving objects is a complex flow problem in reality. Solving complex flow, such as, multi-body separation, aeroelasticity and forced vibration, is a difficulty in CFD. Some more powerful numerical technologies need to be developed to obtain the solutions of complex systems more conveniently and accurately. Remarkable achievements are attained with meshless method in recent decades. Different from grid-based algorithm, meshless method is a numerical algorithm that merely needs nodes information and does not need to connect nodes into mesh cell. This method is suitable for the calculation of complex flow field.Based on the two-dimensional explicit meshless method, method of searching satellite points, dissipation model and method of solving the symmetric equations are improved, and this method is extended to three-dimensional. Accuracy of three-dimensional meshless method is proved based on distribution of orthogonal equidistant discrete points. Accuracy of meshless method is of the same order compared to the traditional difference schemes in the case of same distribution of orthogonal equidistant. Comparison of results obtained by meshless method and difference schemes is given. The results agree well with each other. Proof of accuracy hasn't been demonstrated based on mathematical theory method and discrete point's distribution which isn't orthogonal and equidistant. In the framework of above-mentioned distribution of discrete points, some typical examples with the analytical solution are selected, and solved by meshless method. Numerical results are compared to analytical solutions, respectively. The results show that small relative error is acceptable. High efficient searching satellite point's method is introduced; meshless method is applied to the numerical simulation of NACA0012, projectile in supersonic and B1AC2R generic missile problems etc. Axial/normal force of B1AC2R and lift/drag coefficients are calculated and analyzed in detail. Numerical results are compared with experiment results and corresponding results obtained to other mesh method. Finally, complex flow field of DLR-F4 is obtained with meshless method. The computational results are compared to the experimental results and those obtained by mesh method.On the basis of solving Euler equations, viscous term is added on the right side of Euler equations. N-S equations with laminar flow and S-A turbulence model are solved with meshless method. Calculation of first-order derivative is the same with the calculation in solving Euler equations. Second derivative in viscous term is obtained by fitting twice. Discrete points in boundary layer are generated by advancing-by-layer method. After that, flow fields of NACA0012 in subsonic/transonic and hollow projectile in supersonic are simulated, respectively. Finally, viscous flow of DLR_F4 wing-body configuration and blended wing body aircraft are calculated. The present results are found to be in good agreement with the experimental results. Using the concept of overlapping mesh method for reference, a new method called as Overlapping Clouds of Points Method (OCPM) is firstly proposed to simulate unsteady flow with moving boundary problems based on meshless method. Four cases including piston problem, NACA0012 airfoil vibration, flow around a moving sphere in supersonic and multi-body separation are employed to verify accuracy and practicability of OCPM. This method can be not only applied to the vibration problem with small deformation, but also applied to the multi-bodies separation problem with large deformation. The numerical results agree well with exact solution or experimental results, which shows that the proposed OCPM can be applied to the simulation of unsteady flow problems.Parallel algorithm is employed to the three-dimensional meshless method using Linux and MPI based on the cluster system. According to the characteristics of meshless calculation, the parallel searching of satellite points in the pre-processing stage and parallel algorithm in the main calculation stage are studied by the setting of manually partition and the custom data type of transmission of information. The process of meshless parallel algorithm and authentication examples are given. In order to realize the parallel numerical simulation of three-dimensional complex flow field by overlapping clouds of points method, a parallel algorithm of overlapping clouds of points method is studied. Two different parallel divisional methods are designed according to the characteristics of overlapping clouds of point method. A simple case is performed to validate the two methods. The speedup ratio and parallel efficiency are investigated. The result shows that the parallel meshless algorithm can keep high computational precision and efficiency.The present meshless method thoroughly abandons mesh cell information existing in the traditional mesh and meshless methods. In the simulation of unsteady flow problem, this method only involves movement and calculation of discrete points. Its flexible disposing method is suitable to be used in the flow field simulation. Parallel algorithm designed for meshless method improves the computational efficiency. Meshless method has potential application in solving complex flow simulation and the unsteady flow with moving boundary.