发展了基于四叉树数据结构的网格生成和二维流动的N-S方程数值求解器及动边界问题的Euler方程求解方法.采用压力梯度或者密度梯度的绝对值作为网格自适应的控制参量,同时采用基于最小二乘法的无网格方法处理对于一般Cartesian网格难于处理的物面边界条件.采取了绕方柱流动和绕圆柱流动的经典算例对所发展的方法进行了验证.计算的结果验证了所发展的方法在处理绕流流动时的合理性和有效性.采用Naca0012翼型的几种工况验证了所发展的动网格技术在处理无粘流动的合理性和可行性.从而为数值模拟具有复杂几何外形的流动提供了一种网格布局合理、高效,边界处理简单易行的新思路.%A quadtree-based adaptive Cartesian grid generation and a flow solver for 2-D flow of Navier-Stokes equations and solutions to Euler equation with a moving boundary were developed . The grid adaptation based on pressure or density gradient was performed and a gridless or meshless method based on the least-square fashion was used to treat a wall surface boundary condition handled difficulty with a common Cartesian grid. Firstly, to validate the technique of grid adaptation, the flows over a cube were computed. Secondly, the flows over a cylinder were calculated to validate the developed gridless method. Thirdly, Euler solutions of Naca0012 wing under three working cases were solved and computed with moving grid with gridless method. The computational results indicated the developed methods are reasonable for complex flows. So these methods provides a new idea to simulate flows over objects with complex geometric shepes using more reasonable distribution of grids and easier boundary treatment.
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