China
Africa
Explore chapters and articles related to this topic
Philosophy of Security Assessment
Published in James A. Momoh, Mohamed E. El-Hawary, Electric Systems, Dynamics, and Stability with Artificial Intelligence Applications, 2018
James A. Momoh, Mohamed E. El-Hawary
It is usual for simplicity to maintain a constant step length with these methods if k > 2. Each application of a corrector method improves the accuracy of the method by one order, up to a maximum given by the order of accuracy of the corrector. Therefore, if the corrector is not to be iterated, it is common to use a predictor with an order of accuracy one less than that of the corrector. The predictor is thus not essential as the value at the previous step may be used as a first crude estimate, but the number of iterations of the corrector may be large.
The theory of lossy TLM
Published in Donard de Cogan, Transmission Line Matrix (TLM) Techniques for Diffusion Applications, 2018
Soulos et al [4.16] investigated the increase in order of accuracy for one-dimensional diffusion treated as over-damped wave propagation. Order of accuracy measures how the discretisation error vanishes when the mesh is refined. Variations in Z do not achieve an improvement and for this reason the authors considered a loaded node with a stub-line and resistor (Rs) in series. The left, right and stub voltages can be expressed using the traditional scatter and connect routines. Alternatively, the incident pulses can be expressed in terms of the incident pulses at the previous iteration k+1(iVLiVRiVS)=((1−ρ−τ′)x¯ρx¯τ′x¯ρx(1−ρ−τ′)τ′xτS/2τS/2ρS/2)k(iVLiVRiVS)
Formulation of consistent finite volume schemes for hydraulic transients
Published in Journal of Hydraulic Research, 2019
Sara Mesgari Sohani, Mohamed Salah Ghidaoui
While research in the past 20 years has showed significant potential of transient-based detection methods, only recently has the importance of high frequency waves and model accuracy to defect detection been pointed out (Duan et al., 2012; Stephens et al., 2004). Therefore, it would seem imperative that the numerical models used have a higher order of accuracy. Among the many numerical methods applied to transients (e.g. method of characteristics (MOC), wave plan (WP), finite difference (FD), finite element (FE), finite volume (FV), and corrective smoothed particle method (CSPM)), FV methods are known to be well suited for high frequency waves (Luo & Xu, 2013; Luo, Xuan, & Xu, 2013). However, FV methods have traditionally been formulated only for simple boundary conditions such as the Neumann, Dirichlet or Robin conditions. FV methods have not been formulated for the more complex and ubiquitous types of boundary conditions that are present in pipe systems such as valves, junctions and pumps. Such boundary conditions are generally in the form of pressure-flow relations that are nonlinear, implicit, time-dependent and not rendered easily amenable to the FV framework.
An Optimised Five-Point-Stencil Weighted Compact Nonlinear Scheme for Hyperbolic Conservation Laws
Published in International Journal of Computational Fluid Dynamics, 2021
Zheng Hong, Zhengyin Ye, Kun Ye
Adopting the idea of Fu, Hu, and Adams (2016), the upwind scheme can be optimised by assembling two fourth-order sub-schemes, expressed as is an upwind scheme and is a central non-dissipative scheme, shown as When , the optimal fifth-order upwind scheme, Equation (13), is recovered. The overall scheme gradually biases towards a central scheme as decreases, and thus the dissipation of the overall scheme is reduced, as shown in Figure 1. Under the limitation of in the entire range of wave number, is selected in the present paper. Compared to the fifth-order upwind scheme, the dissipation of Equation (14) is significantly reduced when . It should be pointed out that the order of accuracy of Equation (14) is reduced to fourth order for . The scheme with higher order of accuracy tends to give more accurate result when the resolution of grid is fine enough. However, in realistic calculations especially concerning multi-dimensional problems, grids are relatively coarse due to the limitation of computational cost. For improving the resolution at smooth small-scale flow structures on such grid, reducing excessive dissipation of the scheme is more important than higher order of accuracy.
Adaptive mesh using non-conventional 1D and 2D finite elements based on CUF
Published in Mechanics of Advanced Materials and Structures, 2023
To alleviate meshing issues, more advanced techniques can be used, resorting to numerical methods that are designed from the very beginning to provide arbitrary order of accuracy on more generally shaped elements. These techniques are based on Virtual Element Method (VEM) or Polytopal Element Method (PEM) [17] and can be properly investigated in literature.