Inverting turbulence: flow patterns and parameters from sparse data

在过去的几十年里，我们用尺度解析模拟（如大涡流和直接数值模拟）来计算湍流的能力得到了极大的发展。在这些模拟中，设定了问题参数和边界条件，求解了正演问题。然而，在许多现实环境中，这些信息可能不确定或根本无法获得。对于许多这些湍流的观测数据，如速度或标量测量，可以在几个传感器位置获得。这些传感器可以是静态的，也可以是移动的（例如，监测空气质量的可穿戴设备现在很便宜，而且很容易负担得起）。可用的观测数据可以与控制方程同化，以恢复缺失的信息。这是通过制定和解决一个优化问题来实现的，该问题可以最小化传感器点的估计值和观测值之间的差异。该问题的解提供了满足方程的速度场和标量场，并与现有观测值最优匹配。这就是所谓的逆问题，从这个意义上说，湍流是“反向的”。然而，解决这一优化问题的现有方法要么失败，要么很快变得难以处理湍流（由于所谓的“蝴蝶效应”）。我们的目标是通过制定一种具有可负担的计算成本的新方法来打破僵局，并将其应用于建筑周围的环境问题，流动和污染物扩散。这项努力的成功可以开辟一个新的研究方向，并可以导致全新的技术，如支持案例中更详细地描述的那样。

Our ability to compute turbulent flows with scale-resolving simulations, like Large Eddy and Direct Numerical simulations, has grown tremendously in the past decades. In these simulations, problem parameters and boundary conditions are specified and the forward problem is solved. In many real-life settings however, this information maybe uncertain or not available at all. For many of these turbulent flows observational data, such as velocity or scalar measurements, are available at several sensor locations. These sensors can be either static or mobile (for example wearable devices that monitor air quality are now cheap and easily affordable). The available observational data can be assimilated with the governing equations to recover the missing information. This is achieved by formulating and solving an optimisation problem that minimises the difference between the estimated and observed values at the sensor points. The solution to this problem provides the velocity and scalar fields that satisfy the equations and optimally match with the available observations. This is known as the inverse problem and in this sense turbulence is "inverted". Available methods to solve this optimisation problem however either fail or quickly become intractable for turbulent flows (due to the so called "butterfly effect"). We aim to break the impasse by formulating a new approach with affordable computational cost and apply it to an environmental problem, flow and pollutant dispersion around a building. Success in this endeavour can open a new direction of research, and can lead to entirely new technologies, as described in more detail in the case of support.