Abstract
In spite of the inherent difficulty, reproducing the exact structure of real flows is a critically important issue in many fields, such as weather forecasting or feedback flow control. In order to obtain information on real flows, extensive studies have been carried out on methodology to integrate measurement and simulation, for example, the four-dimensional variational data assimilation method (4D-Var) or the state estimator such as the Kalman filter or the state observer. Measurement-integrated (MI) simulation is a state observer in which a computational fluid dynamics (CFD) scheme is used as a mathematical model of the physical system instead of a small dimensional linear dynamical system usually used in state observers. A large dimensional nonlinear CFD model makes it possible to accurately reproduce real flows for properly designed feedback signals. This review article surveys the theoretical formulations and applications of MI simulation. Formulations of MI simulation are presented, including governing equations of a flow field observer, those of a linearized error dynamics describing the convergence of the observer, and stabilization of the numerical scheme, which is important in implementation of MI simulation. Applications of MI simulation are presented ranging from fundamental turbulent flows in pipes and Karman vortices in a wind tunnel to clinical application in diagnosis of blood flows in a human body.
Highlights
Recent advances in computational fluid dynamics (CFD) enable calculation of complex flows appearing in many practical applications with reasonable accuracy
In numerical simulation used for weather forecasting, the initial condition is updated at time intervals based on past computational results and measurement data around the computational grid points
Applications of MI simulation are presented ranging from fundamental turbulent flow in pipes [1] [13] [23] and Karman vortices in a wind tunnel [14] [24] to clinical application of diagnosis of blood flows in the human body [16] [25]-[27]
Summary
Recent advances in computational fluid dynamics (CFD) enable calculation of complex flows appearing in many practical applications with reasonable accuracy. The present author [13] proposed a measurement-integrated simulation (hereafter abbreviated as “MI simulation”), which is a kind of observer using a CFD scheme as the mathematical model of a relevant system, and successfully applied it to a turbulent flow in a square duct, a Karman vortex street behind a square cylinder [14] [15], and blood flow in an aneurismal aorta [16]. A large dimensional nonlinear CFD model makes it difficult to design the feedback law in a theoretical manner; it has been determined by a trial-and-error method based on physical considerations. It makes it possible to accurately reproduce real flows once the feedback law is properly designed.
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