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Simulating Flood Due to Dam Break
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Ali Ersin Dinçer, Zafer Bozkuş, Ahmet Nazım Şahin, Abdullah Demir, Saeid Eslamian
The domain of the problem is generally bounded for most engineering applications. Therefore, boundary conditions play a vital role in numerical simulations. In SPH, equations may not be valid near the boundaries due to the truncation of the kernel when the particle is near the boundary. In addition, in some cases, the penetration of the particles may not be prevented. Consequently, the application of the boundary conditions, especially solid wall boundary, to SPH is problematic and is an ongoing subject. Two main boundary models to represent solid wall boundary are usually used in SPH. In the first model, boundary particles are placed at the boundary to complete the kernel estimation of the fluid particles near the boundary. Boundary particles also exert a repulsive force to the fluid particles approaching the boundary. The force exerted increases while the distance between the fluid and boundary particle decreases. This force-based method was firstly derived by Monaghan (1994). He proposed to use Lennard-Jones forces as the boundary conditions. Then, Monaghan and Kos (1999) calculated the forces exerted by boundary particles in terms of normal and tangential vectors of fluid particles. In this method, the particles traveling parallel to the boundary do not feel a force in contrast to the previous method of Monaghan and so parallel motion is not disturbed. Ferrand et al. (2010) renormalized the smoothing calculation for the missing kernel area at the boundary domain. The computational time for this method is higher because, in the renormalization process, geometrical quantities change with time.
Applied Sensitivity Problems
Published in Efim Rosenwasser, Rafael Yusupov, Sensitivity of Automatic Control Systems, 2019
Efim Rosenwasser, Rafael Yusupov
The first class incorporates problems where the insensitivity constraints are formalized in the form of constraints imposed on additional motion or sensitivity function. As a special case, these restrictions can be expressed by Relations (8.76)–(8.81). Control systems that are designed using these kinds of restrictions will be called systems with bounded sensitivity. Depending on the specific type of constraints, it is expedient to separate problems of designing parametrically invariant systems (constraints (8.76)), parametrically invariant up to ϵ (see (8.77)), systems with zero sensitivity (see (8.78)), systems with ϵ-sensitivity (see (8.79)), etc.
Laplace transform
Published in Alexander D. Poularikas, ®, 2018
Observe that there is no damping, and the response is thus a sustained oscillatory function. Such a system has a bounded response to a bounded input, and the system is defined as stable even though it is oscillatory.
Decentralised robust tracking and model following for uncertain large-scale interconnected systems with time-varying delays and dead-zone inputs
Published in International Journal of Systems Science, 2021
For mathematical completeness, it is supposed that the initial condition of each subsystem with time-delay is given by where is a given uniformly continuous and bounded function on , and where Here, for our decentralised tracking control problem, the local reference signal , which is followed by the output of each subsystem of large-scale interconnected systems, is assumed to be the output of a local delay-free reference model in the form of where for , is the state, is the output, and is the input of each local reference model. In addition, , , are the given constant matrices of appropriate dimensions. For an output tracking control problem, should be assumed to have the same dimension as , i.e. . In general, for any practical control problem, the model state should be required to be bounded. Thus, we can assume that for each local reference model, there exists a finite positive constant such that for any , . Moreover, the bound of the input vector of each local reference model is described by , where is any positive constant.