Evaluation of the local error of fractional-rational multistep methods with variable integration step

2011 ◽  
Vol 178 (4) ◽  
pp. 399-408 ◽  
Author(s):  
R. V. Slonevsky ◽  
R. R. Stolyarchuk
Keyword(s):  
Multistep Methods ◽  
Local Error ◽  
Integration Step ◽  
Variable Integration

scholarly journals The influence of auger wear on the parameters of the dehydration process of solid waste in the garbage truck

2021 ◽  
Vol 100 (2) ◽  
pp. 79-86
Author(s):  
O. Bereziuk ◽  
◽  
V. Savulyak ◽  
V. Kharzhevskyi ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Energy Consumption ◽  
Angular Velocity ◽  
Solid Waste ◽  
Working Fluid ◽  
Integration Step ◽  
Dehydration Process ◽  
Hydraulic Motor ◽  
Variable Integration ◽  
The Cost

The article is dedicated to the study of the influence of auger wear on the parameters of the dehydration process of municipal solid waste in the garbage truck. An improved mathematical model of the drive operation of dehydration of solid waste in the garbage truck is proposed, which takes into account the wear of the auger and allowed to numerically determine the dynamics of the drive during start-up. It was also established that increasing wear of the auger, the pressure of the working fluid at the inlet of the hydraulic motor rises, and the angular velocity and speed of the auger is significantly reduced. The research of this mathematical model was carried out using the numerical Runge-Kutta-Felberg method of the 4th order with a variable integration step. By means of the method of regression analysis, the power dependencies of the change of nominal values ​​of pressures at the inlet of the hydraulic motor, angular velocity and speed of rotation of the auger from the value of its wear are determined. The last-mentioned dependence defines the detuning from the optimal speed of the auger during its wear and is used to determine the energy consumption of dehydration of solid waste, taking into account the wear of the auger. It is established that the wear of the auger by 1000 mm leads to an increase in the energy consumption of dehydration of solid waste by 11.6%, and, therefore, also leads to an increase of the cost of the process of their dehydration in the garbage truck. It was also established the expediency of further research to determine the appropriate material of the auger and the ways to increase its wear resistance.

scholarly journals Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2463
Author(s):  
Aleksandra Tutueva ◽  
Denis Butusov
Keyword(s):  
Numerical Stability ◽  
Large Scale ◽  
Integration Step ◽  
Variable Integration ◽  
Predicted Values ◽  
Low Dimensional ◽  
Three Body ◽  
Systems Simulation ◽  
Predictor Corrector

The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

scholarly journals Modeling the Influence of Engine Dynamics on Its Indicator Diagram

Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 7885
Author(s):  
Piotr Deuszkiewicz ◽  
Jacek Dziurdź ◽  
Paweł Fabiś
Keyword(s):  
Rotational Speed ◽  
Digital Signal ◽  
Position Angle ◽  
Acceleration Process ◽  
Integration Step ◽  
Angle Sensor ◽  
Indicator Diagram ◽  
Work Cycle ◽  
Variable Integration ◽  
Pressure Changes

This article presents a proposal to describe the pressure changes in the combustion chamber of an engine as a function of the angle of rotation of the crankshaft, taking into account changes in rotational speed resulting from acceleration. The aim of the proposed model is to determine variable piston forces in simulation studies of torsional vibrations of a crankshaft with a vibration damper during the acceleration process. Its essence is the use of a Fourier series as a continuous function to describe pressure changes in one cycle of work. Such a solution is required due to the variable integration step during the simulation. It was proposed to determine the series coefficients on the basis of a Fourier transform of the averaged waveform of a discreet open indicator diagram, calculated for the registration of successive cycles. Recording of the indicative pressure waveforms and shaft angle sensor signals was carried out during tests on the chassis dynamometer. An analysis of the influence of the adopted number of series coefficients on the representation of signal energy was carried out. The model can also take into account the phenomenon of work cycle uniqueness by introducing random changes in the coefficients with magnitudes set on the basis of determined standard deviations for each coefficient of the series. An indispensable supplement to the model is a description of changes in the engine rotational speed, used as a control signal for the PID controller in the simulation of the load performed by the dynamometer. The accuracy of determining the instantaneous rotational speed was analyzed on the basis of signals from the crankshaft position angle sensor and the piston top dead center (TDC) sensor. Limitations resulting from the parameters of digital signal recording were defined.

A Finite Element Model of Hydraulic Pipelines using an Optimized Interlacing Grid System

1993 ◽  
Vol 207 (4) ◽  
pp. 213-222 ◽  
Author(s):  
K Sanada ◽  
C W Richards ◽  
D K Longmore ◽  
D N Johnston
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Natural Frequencies ◽  
Element Model ◽  
Integration Step ◽  
Grid System ◽  
Time Domain Simulation ◽  
Optimized Model ◽  
Variable Integration ◽  
System Frequency

Simulation of flow and pressure variations in fluid pipelines using finite difference and finite element models can give unrealistic results, corresponding to errors in natural frequencies. A novel finite element model of hydraulic pipelines has been developed, using an interlacing grid system. The grid spacing is non-uniform and is optimized, using a genetic algorithm, to make some or all of the undamped natural frequencies of the model as close as possible to exact theoretical ones for a uniform pipe with the extreme boundary conditions of either constant pressure or no flow. Inaccuracies in the highest natural frequencies may be acceptable because of the effect of frequency-dependent friction and limited system frequency response. The optimized model gives accurate results in time domain simulation, and it allows variable properties and a variable integration step to be readily accommodated.

Continuous Digital Simulation of the Second-Order Slowly Varying Wave Drift Force

1980 ◽  
Vol 24 (03) ◽  
pp. 181-189
Author(s):  
B. W. Oppenheim ◽  
P. A. Wilson
Keyword(s):  
Discrete Series ◽  
Digital Simulation ◽  
Second Order ◽  
Integration Step ◽  
Step Size ◽  
Cosine Series ◽  
Wave Drift ◽  
Drift Force ◽  
Variable Integration ◽  
Force Time

A discussion is given on practical aspects of digital representation in time of the slowly oscillatory second-order wave drift force from a known force spectrum. The emphasis is placed on the computational efficiency and on the suitability of the simulation to a numerical integration of an equation of motion using a variable integration step size, where the force acts as the excitation of motion. The effect of approximating the original spectrum by a white spectrum is discussed. A sensitivity analysis is made to the range of frequencies of the spectra. The force time record is obtained by first generating at equal time intervals a discrete time series which possesses the desired random characteristics, and then by extending the discrete series into a continuously available digital record using a sin(x)/x-type interpolation. Various numerical tests are illustrated with plots. Superiority of the fast Fourier transform over the cosine series is demonstrated in terms of the spectral contents preservation.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

scholarly journals The On-Line Integrated Mesoscale Chemistry Model BOLCHEM

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 192
Author(s):  
Rita Cesari ◽  
Tony Christian Landi ◽  
Massimo D’Isidoro ◽  
Mihaela Mircea ◽  
Felicita Russo ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Transport Model ◽  
Horizontal Resolution ◽  
Integration Step ◽  
Chemistry Transport Model ◽  
European Environmental Agency ◽  
On Line ◽  
One Year ◽  
Pm2.5 And Pm10 ◽  
Monitoring Service

This work presents the on-line coupled meteorology–chemistry transport model BOLCHEM, based on the hydrostatic meteorological BOLAM model, the gas chemistry module SAPRC90, and the aerosol dynamic module AERO3. It includes parameterizations to describe natural source emissions, dry and wet removal processes, as well as the transport and dispersion of air pollutants. The equations for different processes are solved on the same grid during the same integration step, by means of a time-split scheme. This paper describes the model and its performance at horizontal resolution of 0.2∘× 0.2∘ over Europe and 0.1∘× 0.1∘ in a nested configuration over Italy, for one year run (December 2009–November 2010). The model has been evaluated against the AIRBASE data of the European Environmental Agency. The basic statistics for higher resolution simulations of O3, NO2 and particulate matter concentrations (PM2.5 and PM10) have been compared with those from Copernicus Atmosphere Monitoring Service (CAMS) ensemble median. In summer, for O3 we found a correlation coefficient R of 0.72 and mean bias of 2.15 over European domain and a correlation coefficient R of 0.67 and mean bias of 2.36 over Italian domain. PM10 and PM2.5 are better reproduced in the winter, the latter with a correlation coefficient R of 0.66 and the mean bias MB of 0.35 over Italian domain.

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