【作者】 马志华；

【导师】 陈红全；

【作者基本信息】 南京航空航天大学 ， 流体力学， 2008， 博士

【摘要】 无网格方法具有布点灵活性,适合处理复杂外形,但和基于网格的算法相比在计算效率上还不具竞争性。为了提高计算效率并集现有方法各自的特点于一体,本文结合各种管道内流、绕翼型外流及反设计等实际问题,就自适应无网格及网格和无网格混合算法等相关问题开展了深入系统的研究。首先对无网格算法基本控制单元,即点云结构的概念进行了介绍。在点云结构上空间导数拟合是采用无网格方法首先所要解决的问题,本文运用最小二乘和移动最小二乘方法的原理,使空间导数拟合问题归结为与点云结构密切相关的线性方程组求解问题;分析和讨论了几种较为常见的选点准则,提出了综合选点构造点云结构的方法,有效地避免了可能出现的线性方程组病态问题。其次研究了用于求解Euler方程的无网格算法。对于翼型后缘等物面边界以及远场边界,提出了适合点云结构的边界条件处理方法。借鉴网格方法中常见的逆风格式和人工耗散模型,构造了适合点云结构的对应处理方法,由此提出求解Euler方程的具体实施方法,并成功地对绕翼型跨音速及超音速典型流动问题进行了数值模拟,为进一步开展无网格自适应以及网格和无网格混合算法的研究打下了基础。接着研究了自适应无网格算法,以期降低初始布点要求和提高计算效率。提出了基于点云结构的局部加密技术:利用压力梯度探测流场中出现激波的敏感区域,并在这些区域中生成新节点,形成更加精细的点云结构;为进一步控制计算节点总数,提出了自适应节点移动方法:根据点云结构参考半径均布的思想,以压力梯度构造权函数来控制点云的参考半径,通过减小敏感区域内点云的参考半径,实现了节点向流动特征的自适应移动。算例展示出本文发展的自适应方法能使节点的位置或者数量进行合理的调整,激波等流场特征分辨率有了显著提高。为充分利用无网格方法灵活的优点并且最大限度减少它所需付出的计算工作量,本文进一步提出了基于局部无网格技术的网格与无网格混合算法。与单一的无网格方法相比较,由于在大部分计算区域采用了网格单元填充,使得发展的算法在运算效率上能与网格方法相当;同时在物体附近嵌入了无网格区,只要求局部布点离散,具有灵活性,使得发展的算法适合处理任意外形。在网格与无网格区域的交界处,提出了布置辅助单元和节点等方法构成边界信息,实现了区域间的流动信息传递。控制方程的空间导数分别在两区域用有限体积法和无网格法离散近似,时间方向都采用四步显式Runge-Kutta格式推进求解,数值模拟了喷管内部和绕翼型外部等二维定常流动问题,在此基础上将混合算法推广用于三维非定常流动问题的求解,并分别与整体有限体积法和整体无网格方法进行了比较。算例展示出,本文提出的混合算法能有效捕捉激波间断,且两区域等值线过渡光滑,算法效率如预期与网格算法相当,表明方法是可行的。最后,本文利用发展的混合算法与遗传算法结合,进行了反设计问题的尝试性研究,展示出本文发展的方法在处理工程实际问题中所具有的潜力和良好的应用前景。更多还原

【Abstract】 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.更多还原