A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations
A self-organizing Lagrangian particle method for adaptive-resolution advection-diffusion simulations
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DOI：
10.1016/j.jcp.2012.01.026
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
S. Reboux;Birte Schrader;I. Sbalzarini
中科院分区：
文献类型：
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作者：
S. Reboux;Birte Schrader;I. Sbalzarini
提出了一种新的求解连续抛物问题的自适应分辨率粒子方法。在该方法中，粒子自组织以适应局部分辨率要求。这是通过伪力来实现的，这些伪力被设计成确保溶液总是被良好地采样，并且在颗粒分布中没有空穴或簇。颗粒尺寸局部适应于溶液的长度尺度。微分算子一致的评价不规则分布的粒子的大小不同，使用离散化校正的运营商的不断发展的集合。该方法不依赖于任何全局变换或映射函数。在介绍了该方法及其误差分析，我们证明了它的能力和局限性的一组二维和三维基准问题。这些方法包括对流扩散、Burgers方程、Buckley-Leverett五点问题和曲率驱动的水平集曲面精化。
We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection–diffusion, the Burgers equation, the Buckley–Leverett five-spot problem, and curvature-driven level-set surface refinement.