Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Ming Wei ◽  
Yonghong Wang ◽  
Huafen Song
Keyword(s):  
Numerical Stability ◽  
Rounding Error ◽  
One Dimensional ◽  
Flow Models ◽  
Numerical Stability Analysis ◽  
Last Stage ◽  
The Stability ◽  
Performance Calculation ◽  
Poor Stability ◽  
Input Error

Sensitivity and numerical stability of an algorithm are two of the most important criteria to evaluate its performance. For all published turbine flow models, except Wang method, can be named the “top-down” method (TDM) in which the performance of turbines is calculated from the first stage to the last stage row by row; only Wang method originally proposed by Yonghong Wang can be named the “bottom-up” method (BUM) in which the performance of turbines is calculated from the last stage to the first stage row by row. To find the reason why the stability of the two methods is of great difference, the Wang flow model is researched. The model readily applies to TDM and BUM. How the stability of the two algorithms affected by input error and rounding error is analyzed, the error propagation and distribution in the two methods are obtained. In order to explain the problem more intuitively, the stability of the two methods is described by geometrical ideas. To compare with the known data, the performance of a particular type of turbine is calculated through a series of procedures based on the two algorithms. The results are as follows. The more the calculating point approaches the critical point, the poorer the stability of TDM is. The poor stability can even cause failure in the calculation of TDM. However, BUM has not only good stability but also high accuracy. The result provides an accurate and reliable method (BUM) for estimating the performance of turbines, and it can apply to all one-dimensional performance calculation method for turbine.

Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines

2013 ◽  
Author(s):  
Ming Wei ◽  
Yonghong Wang ◽  
Huafen Song
Keyword(s):  
Numerical Stability ◽  
Rounding Error ◽  
One Dimensional ◽  
Flow Models ◽  
Numerical Stability Analysis ◽  
Last Stage ◽  
The Stability ◽  
Performance Calculation ◽  
Poor Stability ◽  
Input Error

Sensitivity and numerical stability of an algorithm are two of the most important criteria to evaluate its performance. For all published turbine flow models, except Wang method, can be named the ‘top-down’ method (TDM) in which the performance of turbines is calculated from the first stage to the last stage row by row; only Wang method originally proposed by Yonghong Wang can be named the ‘bottom-up’ method (BUM) in which the performance of turbines is calculated from the last stage to the first stage row by row. To find the reason why the stability of the two methods is of great difference, the Wang flow model is researched. The model readily applies to TDM and BUM. How the stability of the two algorithms affected by input error and rounding error is analyzed, the error propagation and distribution in the two methods are obtained. In order to explain the problem more intuitively, the stability of the two methods is described by geometrical ideas. To compare with the known data, the performance of a particular type of turbine is calculated through a series of procedures based on the two algorithms. The results are as follows. The closer the operating point approaches the critical point, the poorer the stability of TDM is. The poor stability can even cause failure in the calculation of TDM. However BUM has not only good stability, but also high accuracy. The result provides an accurate and reliable method (BUM) for estimating the performance of turbines, and it can apply to all one-dimensional performance calculation method for turbine.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Stability of a one-dimensional morphoelastic model for post-burn contraction

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Ginger Egberts ◽  
Fred Vermolen ◽  
Paul van Zuijlen
Keyword(s):  
Wound Healing ◽  
Residual Stresses ◽  
Truncation Error ◽  
Signaling Molecules ◽  
Discrete Problem ◽  
One Dimensional ◽  
Stability Constraint ◽  
Biological Interpretation ◽  
The Stability ◽  
The One

AbstractTo deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular densities of fibroblasts and myofibroblasts, and the density of collagen. Here we present stability constraints for the one-dimensional counterpart of this morphoelastic model, for both the continuous and (semi-) discrete problem. We show that the truncation error between these eigenvalues associated with the continuous and semi-discrete problem is of order $${{\mathcal {O}}}(h^2)$$ O ( h 2 ) . Next we perform numerical validation to these constraints and provide a biological interpretation of the (in)stability. For the mechanical part of the model, the results show the components reach equilibria in a (non) monotonic way, depending on the value of the viscosity. The results show that the parameters of the chemical part of the model need to meet the stability constraint, depending on the decay rate of the signaling molecules, to avoid unrealistic results.

scholarly journals One-Dimensional Organic–Inorganic Material (C6H9N2)2BiCl5: From Synthesis to Structural, Spectroscopic, and Electronic Characterizations

2021 ◽  
Vol 22 (4) ◽  
pp. 2030
Author(s):  
Hela Ferjani ◽  
Hammouda Chebbi ◽  
Mohammed Fettouhi
Keyword(s):  
Hydrogen Bonding ◽  
Density Functional ◽  
Crystal Packing ◽  
Diffuse Reflectance Spectrum ◽  
Enrichment Ratio ◽  
One Dimensional ◽  
Organic Part ◽  
Fukui Indices ◽  
The Stability ◽  
The One

The new organic–inorganic compound (C6H9N2)2BiCl5 (I) has been grown by the solvent evaporation method. The one-dimensional (1D) structure of the allylimidazolium chlorobismuthate (I) has been determined by single crystal X-ray diffraction. It crystallizes in the centrosymmetric space group C2/c and consists of 1-allylimidazolium cations and (1D) chains of the anion BiCl52−, built up of corner-sharing [BiCl63−] octahedra which are interconnected by means of hydrogen bonding contacts N/C–H⋯Cl. The intermolecular interactions were quantified using Hirshfeld surface analysis and the enrichment ratio established that the most important role in the stability of the crystal structure was provided by hydrogen bonding and H···H interactions. The highest value of E was calculated for the contact N⋯C (6.87) followed by C⋯C (2.85) and Bi⋯Cl (2.43). These contacts were favored and made the main contribution to the crystal packing. The vibrational modes were identified and assigned by infrared and Raman spectroscopy. The optical band gap (Eg = 3.26 eV) was calculated from the diffuse reflectance spectrum and showed that we can consider the material as a semiconductor. The density functional theory (DFT) has been used to determine the calculated gap, which was about 3.73 eV, and to explain the electronic structure of the title compound, its optical properties, and the stability of the organic part by the calculation of HOMO and LUMO energy and the Fukui indices.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

2014 ◽  
Vol 42 (5) ◽  
pp. 1012-1023 ◽  
Author(s):  
Paris Perdikaris ◽  
George Em. Karniadakis
Keyword(s):  
Blood Flow ◽  
Fractional Order ◽  
One Dimensional ◽  
Flow Models ◽  
Blood Flow Models
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