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首页> 外文期刊>Journal of Computational Physics >A high resolution spatially adaptive vortex method for separating flows. Part I: Two-dimensional domains
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A high resolution spatially adaptive vortex method for separating flows. Part I: Two-dimensional domains

机译：一种用于分离流的高分辨率空间自适应涡旋方法。第一部分：二维域

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摘要

A grid-free high-resolution spatially-adaptive vortex method for two-dimensional incompressible flow in bounded domains is presented. The computational algorithm is based on operator splitting in which convection and diffusion are handled separately every time step. In the convection step, computational elements are convected with velocities obtained by fast approximations of the Biot–Savart superposition with second-order Runge–Kutta time integration scheme. Diffusion is performed using the smooth redistribution method that employs a Gaussian basis function for vorticity in the interior. Near solid walls, the core functions are modified to conserve circulation. The no-slip boundary condition is enforced by creating of a vortex sheet that is redistributed to neighboring elements using the redistribution method. The proposed method enables accurate and smooth recovery of the vorticity and does not require explicit use of vortex images or occasional re-meshing. Algorithms for reduction in computational cost by accurately removing elements in overcrowded regions and for spatial adaptivity that allows for variable core sizes and variable element spacing are presented. Computations of flow around an impulsively started cylinder for Reynolds number values of 1000, 3000, and 9500 are preformed to investigate various aspects of the proposed method.
机译：提出了有界域中二维不可压缩流的无网格高分辨率空间自适应涡旋方法。该计算算法基于运算符拆分，其中对流和扩散在每个时间步分别进行处理。在对流步骤中，计算元素与通过二阶Runge-Kutta时间积分方案对Biot-Savart叠加的快速逼近获得的速度对流。使用平滑重新分配方法执行扩散，该方法采用高斯基函数实现内部涡旋。在实心墙附近，对核心功能进行了修改以节省循环。防滑边界条件是通过创建涡旋表来实施的，该涡旋表使用重新分配方法重新分配给相邻元素。所提出的方法能够准确而平稳地恢复涡度，并且不需要明确使用涡旋图像或偶尔重新划分网格。提出了通过精确去除拥挤区域中的元素来降低计算成本以及可实现可变芯尺寸和可变元素间距的空间适应性的算法。雷诺数分别为1000、3000和9500的脉冲启动汽缸周围的流量的计算是为了研究所提出方法的各个方面而进行的。

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