The Difference-Quotient Turbulence Model (DQTM)

2020 ◽  
pp. 107-172
Author(s):  
Peter William Egolf ◽  
Kolumban Hutter
Keyword(s):  
Turbulence Model ◽  
Difference Quotient ◽  
The Difference

On the Riemann Derivatives for Integrable Functions

1954 ◽  
Vol 6 ◽  
pp. 572-581 ◽  
Author(s):  
P. L. Butzer ◽  
W. Kozakiewicz
Keyword(s):  
Difference Quotient ◽  
Central Difference ◽  
Integrable Functions ◽  
The Difference ◽  
Image Position

The central difference of order s of the function f(x), Δs2hf(x), corresponding to a number h > 0, is defined inductively by the relations.If the limit of the difference quotientexists at the point x, it is called the sth Riemann derivative or the generalized sth derivative of fix) at the point x.

GIM(1) Model and its Application

2011 ◽  
Vol 219-220 ◽  
pp. 432-435
Author(s):  
Bin Zeng ◽  
Wu Jun Zeng
Keyword(s):  
System Application ◽  
Grey Model ◽  
Difference Quotient ◽  
Grey System ◽  
The Difference

Although the GM(1,1) model has been successfully adopted in various fields and has been demonstrated promising prospect. The paper adopts different form of grey model which is a supplement of the grey model and we call it GIM(1) model. On the analyzing the unequal GM(1,1) model the paper uses the difference quotient method to establish the unequal interval GIM(1) model. The examples prove the method in the paper is effective which improves the accuracy of the grey model. It provides an effective way for the grey system application.

scholarly journals Characterization of generalized Orlicz spaces

2018 ◽  
Vol 22 (02) ◽  
pp. 1850079 ◽  
Author(s):  
Rita Ferreira ◽  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Orlicz Spaces ◽  
Difference Quotient ◽  
Variable Exponent Spaces ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz–Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.

scholarly journals Formalizing Calculus without Limit Theory in Coq

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1377
Author(s):  
Yaoshun Fu ◽  
Wensheng Yu
Keyword(s):  
Mathematical Theory ◽  
Control Function ◽  
Taylor Formula ◽  
Difference Quotient ◽  
Fundamental Theory ◽  
Limit Theory ◽  
Leibniz Formula ◽  
New Form ◽  
The Difference ◽  
Definition Of

Formal verification of mathematical theory has received widespread concern and grown rapidly. The formalization of the fundamental theory will contribute to the development of large projects. In this paper, we present the formalization in Coq of calculus without limit theory. The theory aims to found a new form of calculus more easily but rigorously. This theory as an innovation differs from traditional calculus but is equivalent and more comprehensible. First, the definition of the difference-quotient control function is given intuitively from the physical facts. Further, conditions are added to it to get the derivative, and define the integral by the axiomatization. Then some important conclusions in calculus such as the Newton–Leibniz formula and the Taylor formula can be formally verified. This shows that this theory can be independent of limit theory, and any proof does not involve real number completeness. This work can help learners to study calculus and lay the foundation for many applications.

scholarly journals On turbulence models and lidar measurements for wind turbine control

2021 ◽  
Vol 6 (6) ◽  
pp. 1491-1500
Author(s):  
Liang Dong ◽  
Wai Hou Lio ◽  
Eric Simley
Keyword(s):  
Wind Turbine ◽  
Turbulence Model ◽  
Spatial Coherence ◽  
Turbulence Models ◽  
Lidar Measurement ◽  
Wind Turbine Control ◽  
Comprehensive Information ◽  
The Difference ◽  
Turbine Design ◽  
The Impact

Abstract. To provide comprehensive information that will assist in making decisions regarding the adoption of lidar-assisted control (LAC) in wind turbine design, this paper investigates the impact of different turbulence models on the coherence between the rotor-effective wind speed and lidar measurement. First, the differences between the Kaimal and Mann models are discussed, including the power spectrum and spatial coherence. Next, two types of lidar systems are examined to analyze the lidar measurement coherence based on commercially available lidar scan patterns. Finally, numerical simulations have been performed to compare the lidar measurement coherence for different rotor sizes. This work confirms the association between the measurement coherence and the turbulence model. The results indicate that the lidar measurement coherence with the Mann turbulence model is lower than that with the Kaimal turbulence model. In other words, the potential value creation of LAC based on simulations during the wind turbine design phase, evaluated using the Kaimal turbulence model, will be diminished if the Mann turbulence model is used instead. In particular, the difference in coherence is more significant for larger rotors. As a result, this paper suggests that the impacts of different turbulence models should be considered uncertainties while evaluating the benefits of LAC.

scholarly journals Toward a Difference Approach: A Discrete Meat Demand System

2020 ◽  
Vol 5 (3) ◽  
pp. p66
Author(s):  
Shu Tsuchida
Keyword(s):  
Budget Constraint ◽  
Demand System ◽  
Difference Quotient ◽  
Fresh Meat ◽  
Partial Difference ◽  
Meat Demand ◽  
Differential Approach ◽  
The Difference ◽  
Almost All ◽  
Continuous Demand

While the differential approach to economic analysis is useful, the difference approach is indispensable as almost all economic data are discrete, rather than continuous. Thus, we must to investigate the integration of the differential with difference approaches. We show a difference quotient corresponding to a differential quotient, which is generally called a derivative, and a partial difference quotient corresponding to a partial differential quotient, which is generally called a partial derivative. From these, the difference approach produces a discrete demand system with logarithmic mean elasticities as parameters that corresponds to a continuous demand system with point elasticities as parameters produced by the differential approach. These systems should satisfy each budget constraint: the former for finite-change variables and the latter for infinitesimal-change variables. Based on these, we consider a discrete meat demand system, apply it to monthly demand for fresh meat in Japan, and estimate it using a weighted RAS method. The estimated demand system has two desirable properties: each estimated demand (theoretical value) of the conditional demand function coincides with each observed demand, and this system satisfies the difference budget constraint.

scholarly journals Numerical airfoil catalogue including 360° airfoil polars and aeroacoustic footprints

2017 ◽  
Author(s):  
Manfred Imiela ◽  
Benjamin Faßmann ◽  
Gerrit Heilers ◽  
Gunther Wilke
Keyword(s):  
Turbulence Model ◽  
Sound Pressure ◽  
Kriging Interpolation ◽  
High Fidelity ◽  
Data Sets ◽  
Bilinear Interpolation ◽  
Aerodynamic Coefficients ◽  
Data Set ◽  
Sst Turbulence Model ◽  
The Difference

Abstract. A methodology is presented for generating 360° airfoil polars and aeroacoustic characteristics by means of CFD and CAA. The aerodynamic procedure is validated against experimental data of the well-known airfoils DU-93-W-210 and DU-97-W-300. While a better prediction of the aerodynamic coefficients in the range of −30° and 30° is achieved by a combination of the k-ω SST turbulence model and a C-topology mesh, for the remaining angles of attack more confidence is gained with the SA negative turbulence model in combination with an O-topology mesh. Therefore the two data sets are subsequently fused to one complete data set using a kriging interpolation approach. The result of ten different airfoils using the proposed method is presented. For providing the aeroacoustic characteristics for a wide operation range four computations and a bilinear interpolation are needed, since the aeroacoustic is dependent on the Mach and Reynolds number. The bilinear interpolation approach is verificated by a comparison between the originally simulated and the emulated result at a fifth computational set for six different airfoils. The corresponding overall sound pressure level (OASPL) for four angles of attack for these airfoils is presented and the difference between a fully turbulent computation and simulations with fixed transition is assessed. The aeroacoustic results further include high-fidelity directivity functions.

New Two-Fluid Turbulence Model Based Numerical Simulation of Flow in a Flat Suddenly Expanding Channel

2021 ◽  
pp. 24-39
Author(s):  
Z.M. Malikov ◽  
M.E. Madaliev
Keyword(s):  
Turbulence Model ◽  
Control Volume ◽  
Difference Approximation ◽  
Flat Channel ◽  
Central Difference ◽  
Fluid Turbulence ◽  
Before And After ◽  
Nonstationary Equations ◽  
The Difference ◽  
Two Fluid

The purpose of the research was to numerically study the structure of the flow in a flat channel in the zone of its sudden step-like expansion. The results of the study are given in the paper. The calculations are carried out with the use of a new two-fluid turbulence model and are based on the numerical solution of a system of nonstationary equations. The profiles of axial velocity and turbulent stress in various sections of the channel before and after the step were obtained, as well as the dependence of the friction coefficient for the lower wall of the channel on the distance after the step. For the difference approximation of the initial equations, the control volume approach was applied; the relationship between the velocities and pressure was found using the SIMPLEC procedure. Meanwhile, the viscosity terms were approximated by the central difference, and for the convective terms the QUICK second-order accuracy scheme was used. To confirm the correctness of the numerical results, we compared them with the experimental data taken from the NASA database for the Reynolds number Re = 36,000. The results obtained using the SA and SST models are also given in the paper. Despite the coarse grid used for numerical calculations, the results based on the new two-fluid turbulence model are not less accurate than the results determined by the RANS models for predicting separated flows in the flat channel in the zone of its sudden backward-facing step expansion

On the variation of Teichmüller's metric

1980 ◽  
Vol 85 (1-2) ◽  
pp. 143-152 ◽  
Author(s):  
Frederick P. Gardiner
Keyword(s):  
Second Derivative ◽  
Difference Quotient ◽  
First Derivative ◽  
The Difference

SynopsisThe main result of this article is the calculation of the first derivative of Teichmüller's metric from an inequality of Reich and Strebel. Furthermore, from the same inequality one is able to calculate information about the difference quotient for the second derivative. From the techniques used here it does not seem possible to determine whether the metric isC2.

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