Research Of Adaptive Meshfree And Hybridized Mesh/Meshfree Methods

Meshfree algorithm flexibly distributes the points in the domain; therefore it is suitable for solving flows over arbitrary configurations. However, its efficiency is still not competent when compared with mesh based methods. In order to make full use of the advantages of meshfree and mesh methods to efficiently solve direct and inverse problems, adaptive meshfree and hybridized mesh/meshfree algorithms are proposed and studied in the present work.Firstly, the concept of cloud of points, which is the basic control unit of meshfree method, is explained in detail. For spatial derivative approximation in a cloud of points is the core of meshfree method, least square and moving least square are used to derive the linear equations related with the cloud of points for computing the spatial derivatives. Several different point-selection strategies for meshfree cloud are introduced and compared, then a new technique which combines these techniques is further proposed to prevent the linear equations be ill-conditioned.Secondly, the meshfree algorithm is studied for solving Euler equations. Appropriate techniques are proposed for clouds of points to deal with the far field and wall boundary conditions. Artificial dissipation model and upwind schemes for mesh method are investigated, and then proper strategies are developed for meshfree method to solve Euler equations. Classical problems of transonic and supersonic flows over airfoils are successfully simulated, and this paves the way for the study of adaptive meshfree and hybridized mesh/meshfree methodsAdaptive meshfree algorithms are further proposed to improve the computation efficiency and point distribution robustness. On the one hind, local refinement technique for cloud of points is proprosed to increase the resolution of flow features: pressure gradient is used to detect the sensitive places in the flow field where the shock waves appear, and then new points are introduced into these regions to generate more fine clouds. On the other hind, in order to control the number of points during computation, a new adaptive algorithm based on the movement of points is proposed: according to the concept of weighted reference radius equidistribution proposed for meshfree clouds, a weight function based on the gradient of pressure is utilized to manipulate the reference radius, and then the adaptive movement of the points is realized by changing the reference radius of clouds. Numerical examples show that the adaptive algorithms are able to adjust the spatial position or the number of the points, and the resolution of flow features is greatly improved.In order to take full advantage of the flexibility of meshfree method and improve the efficiency, a new concept of local meshfree technique is proposed to develop hybridized mesh/meshfree algorithm. Different with complete meshfree method, the hybrid method uses mesh cells to cover most of the flow field so that it is as efficient as mesh method, and only a small number of meshfree clouds are utilized to deal with arbitrary configurations. To accomplish the transmission of flow information between different regions, mirror cell-point and coupled point techniques are proposed to combine the mesh and meshfree algorithms. The spatial derivatives of the governing equations are approximated by finite volume method and meshfree method, respectively. The hybrid method is used to simulate the two-dimensioanl steady internal flows across channels and external flows over airfoils, and then it is extended to solve three-dimensional unsteady flows. The solutions are compared with complete finite volume and meshfree results. Numerical examples show that the hybrid algorithm captures the shock waves accurately, and it is as efficient as mesh method.Finally, the proposed hybrid mesh/meshfree method is coupled with Genetic Algorithms to form a new method to deal with inverse design problems. The present work shows the great potential and promising application of hybrid method for solving engineering problems.