Source Inversion by Forward Integration in Inertial Flows
Source Inversion by Forward Integration in Inertial Flows
复制标题
通过惯性流中的正向积分进行源反演
DOI：
10.1111/cgf.12913
复制
发表时间：
2016
影响因子：
2.5
通讯作者：
H. Theisel
中科院分区：
文献类型：
--
作者：
T. Günther;H. Theisel
惯性粒子是以一定速度行进的有限大小的物体，该速度不同于底层的携带流，即，它们依赖于质量并具有惯性。它们的后向积分在实践中是不可行的，因为初始速度的微小变化会导致恢复位置的极端变化。因此，如果观察到一个惯性粒子，很难恢复它来自哪里。这被称为源反演问题，它在恢复空气或水污染源方面有许多实际应用。惯性轨道存在于更高维的空间速度空间中。在本文中，我们表明，这个空间是只有稀疏的人口。假设惯性粒子以给定的初始速度释放（例如，从静止），粒子可以仅以有限的一组可能的速度到达某个位置。事实上，随着积分持续时间的增加和粒子响应时间的依赖，惯性粒子收敛到一个终端速度。我们表明，一组初始位置，导致相同的位置形成一条曲线。我们通过设计一个导出的向量场来提取这些曲线，在该向量场中，它们表现为切线曲线。最重要的是，导出的向量场仅涉及向前积分的流图梯度，其比向后轨迹更稳定地计算。提取后，我们交互式地可视化域中的曲线，并使用字形显示达到的速度。此外，我们编码的变化率的终端速度沿着的曲线，这给出了一个概念的收敛到终端速度。有了这个，我们提出了第一个解决方案，考虑实际的惯性轨迹的源反演问题。我们将该方法应用于二维和三维域中的定常和非定常流。
Inertial particles are finite‐sized objects traveling with a certain velocity that differs from the underlying carrying flow, i.e., they are mass‐dependent and subject to inertia. Their backward integration is in practice infeasible, since a slight change in the initial velocity causes extreme changes in the recovered position. Thus, if an inertial particle is observed, it is difficult to recover where it came from. This is known as the source inversion problem, which has many practical applications in recovering the source of airborne or waterborne pollutions. Inertial trajectories live in a higher dimensional spatio‐velocity space. In this paper, we show that this space is only sparsely populated. Assuming that inertial particles are released with a given initial velocity (e.g., from rest), particles may reach a certain location only with a limited set of possible velocities. In fact, with increasing integration duration and dependent on the particle response time, inertial particles converge to a terminal velocity. We show that the set of initial positions that lead to the same location form a curve. We extract these curves by devising a derived vector field in which they appear as tangent curves. Most importantly, the derived vector field only involves forward integrated flow map gradients, which are much more stable to compute than backward trajectories. After extraction, we interactively visualize the curves in the domain and display the reached velocities using glyphs. In addition, we encode the rate of change of the terminal velocity along the curves, which gives a notion for the convergence to the terminal velocity. With this, we present the first solution to the source inversion problem that considers actual inertial trajectories. We apply the method to steady and unsteady flows in both 2D and 3D domains.
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