Numerical simulation of real-world flows

Abstract

Obtaining real flow information is important in various fields, but is a difficult issue because measurement data are usually limited in time and space, and computational results usually do not represent the exact state of real flows. Problems inherent in the realization of numerical simulation of real-world flows include the difficulty in representing exact initial and boundary conditions and the difficulty in representing unstable flow characteristics. This article reviews studies dealing with these problems. First, an overview of basic flow measurement methodologies and measurement data interpolation/ approximation techniques is presented. Then, studies on methods of integrating numerical simulation and measurement, namely, four-dimensional variational data assimilation (4D-Var), Kalman filters (KFs), state observers, etc are discussed. The first problem is properly solved by these integration methodologies. The second problem can be partially solved with 4D-Var in which only initial and boundary conditions are control parameters. If an appropriate control parameter capable of modifying the dynamical structure of the model is included in the formulation of 4D-Var, unstable modes are properly suppressed and the second problem is solved. The state observer and KFs also solve the second problem by modifying mathematical models to stabilize the unstable modes of the original dynamical system by applying feedback signals. These integration methodologies are now applied in simulation of real-world flows in a wide variety of research fields. Examples are presented for basic fluid dynamics and applications in meteorology, aerospace, medicine, etc.

Continuum microhaemodynamics modelling using inverse rheology

“…As blood rheology inherently involves the influence of RBC distribution, accounting for the exclusion layer within the optimisation approach under a definition of 'rheology' is appropriate. This method could be considered as a form of data assimilation, as it incorporates experimental and computational inputs to address shortfalls (Hayase 2015). An important distinction is that we do not combine the CFD and experimental data on a case-by-case basis, but rather use the average error between numerical and experimental data sets to choose optimal model parameters, which can then be applied to the main data set without further iteration.…”

Linear and nonlinear sensor placement strategies for mean-flow reconstruction via data assimilation

“…In parallel with the continuation of more classical approaches to address the closure problem in the RANS equations (Durbin 2018), the latter problem is currently revisited through the consideration of alternative strategies which may be interlinked, as will be detailed in the following: uncertainty quantification (Xiao & Cinnella 2019), data assimilation (Lewis, Lakshmivarahan & Dhall 2006) and data-driven modelling (Duraisamy, Iaccarino & Xiao 2019). In particular, data assimilation aims to merge experimental and numerical approaches in order to overcome their inherent limitations, namely the difficulty in accessing the whole state of the flow in experiments (Heitz, Mémin & Schnörr 2010; Suzuki 2012; Gillissen, Bouffanais & Yue 2019) and the lack of knowledge of the inputs and models in numerical simulations (Hayase 2015; Meldi & Poux 2017; Chandramouli, Mémin & Heitz 2020; Da Silva & Colonius 2020; Li et al. 2020).…”

Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

“…In order to reproduce real flows correctly, many studies have been conducted by integrating numerical simulation and measurement [1]. Combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) with a linear combination, Suzuki et al have developed a method that obtains unmeasurable quantities of an unsteady flow such as pressure fields and vorticity distributions [2], and have evaluated the data-assimilation capabilities of the method [3].…”