scholarly journals Numerical Results of Crank-Nicolson and Implicit Schemes to Laplace Equation with Uniform and Non-Uniform Grids

2021 ◽  
Vol 3 (2) ◽  
pp. 122-135
Author(s):  
Mohammad Ghani
Keyword(s):  
Analytical Solution ◽  
Laplace Equation ◽  
Absolute Error ◽  
Numerical Results ◽  
Implicit Method ◽  
Implicit Schemes ◽  
Separable Variable ◽  
Uniform Grids ◽  
The Absolute ◽  
Crank Nicolson

AbstractIn this paper, we investigate the numerical results between Implicit and Crank-Nicolson method for Laplace equation. Based on the numerical results obtained, we get the conclusion that the absolute error of Crank-Nicolson method is smaller than the absolute error of Implicit method for uniform and non-uniform grids which both refer to the analytical solution of Laplace equation obtained by separable variable method.Keywords: Crank-Nicolson; Implicit; Laplace equation; separable variable method; uniform and non-uniform grids. AbstrakDalam makalah ini, kami menyelidiki hasil numerik antara etode Implisit dan Crank-Nicolson untuk persamaan Laplace. Berdasarkan hasil numerik yang diperoleh, kita mendapatkan kesimpulan bahwa kesalahan absolut metode Crank-Nicolson lebih kecil daripada kesalahan absolut metode Implisit untuk grid seragam dan tak-seragam yang keduanya mengacu pada solusi analitik persamaan Laplace yang diperoleh dengan metode separable.Kata kunci: Crank-Nicolson; Implisit; persamaan Laplace; metode variable terpisah; grid seragam dan tak-seragam.

A Natural BEM on Non-Uniform Grids and its Coupling Method with their Moving Mesh Applications

2013 ◽  
Vol 385-386 ◽  
pp. 1913-1916
Author(s):  
Quan Zheng ◽  
Xiu Hui Guo
Keyword(s):  
Laplace Equation ◽  
Convergence Theorem ◽  
Unbounded Domains ◽  
Numerical Results ◽  
Coupling Method ◽  
Moving Mesh ◽  
Uniform Grid ◽  
Uniform Grids ◽  
Moving Mesh Methods

For solving Laplace equation in 2D unbounded domains, a natural BEM on non-uniform grid is derived and its convergence theorem is proved. The moving mesh methods for the NBEM and the NBE-FE coupling method are also studied. Numerical results confirm the efficiency of the methods.

scholarly journals Prediction of One Repetition Maximum Using Reference Minimum Velocity Threshold Values in Young and Middle-Aged Resistance-Trained Males

2021 ◽  
Vol 11 (5) ◽  
pp. 71
Author(s):  
John F. T. Fernandes ◽  
Amelia F. Dingley ◽  
Amador Garcia-Ramos ◽  
Alejandro Perez-Castilla ◽  
James J. Tufano ◽  
...  
Keyword(s):  
Bench Press ◽  
Absolute Error ◽  
Young Group ◽  
Middle Aged ◽  
Repetition Maximum ◽  
Back Squat ◽  
Velocity Threshold ◽  
Low Load ◽  
The Absolute ◽  
Minimum Velocity

Background: This study determined the accuracy of different velocity-based methods when predicting one-repetition maximum (1RM) in young and middle-aged resistance-trained males. Methods: Two days after maximal strength testing, 20 young (age 21.0 ± 1.6 years) and 20 middle-aged (age 42.6 ± 6.7 years) resistance-trained males completed three repetitions of bench press, back squat, and bent-over-row at loads corresponding to 20–80% 1RM. Using reference minimum velocity threshold (MVT) values, the 1RM was estimated from the load-velocity relationships through multiple (20, 30, 40, 50, 60, 70, and 80% 1RM), two-point (20 and 80% 1RM), high-load (60 and 80% 1RM) and low-load (20 and 40% 1RM) methods for each group. Results: Despite most prediction methods demonstrating acceptable correlations (r = 0.55 to 0.96), the absolute errors for young and middle-aged groups were generally moderate to high for bench press (absolute errors = 8.2 to 14.2% and 8.6 to 20.4%, respectively) and bent-over-row (absolute error = 14.9 to 19.9% and 8.6 to 18.2%, respectively). For squats, the absolute errors were lower in the young group (5.7 to 13.4%) than the middle-aged group (13.2 to 17.0%) but still unacceptable. Conclusion: These findings suggest that reference MVTs cannot accurately predict the 1RM in these populations. Therefore, practitioners need to directly assess 1RM.

Experimental and numerical investigations on a high-density polyethylene (HDPE) blown film cooling with a new design of the counter-flow/radial jet air-ring

2021 ◽  
pp. 875608792110260
Author(s):  
ME Ismail ◽  
MM Awad ◽  
AM Hamed ◽  
MY Abdelaal ◽  
EB Zeidan
Keyword(s):  
Heat Transfer ◽  
Numerical Simulations ◽  
Film Cooling ◽  
Radiation Heat Transfer ◽  
Absolute Error ◽  
Numerical Results ◽  
Upper Lip ◽  
Original Design ◽  
Blown Film ◽  
Set Up

This study experimentally and numerically investigates a typical HDPE blown film production process cooled via a single-lip air-ring. The processing observations are considered for the proposed subsequent modifications on the air-ring design and the location relative to the die to generate a radial jet, directly impinging on the bubble. Measurements are performed to collect the actual operating parameters to set up the numerical simulations. The radiation heat transfer and the polymer phase change are considered in the numerical simulations. The velocity profile at the air-ring upper-lip is measured via a five-hole Pitot tube to compare with the numerical results. The comparison between the measurements and the numerical results showed that the simulations with the STD [Formula: see text] turbulence model are more accurate with a minimum relative absolute error (RAE) of 1.6%. The numerical results indicate that the peak Heat Transfer Coefficient (HTC) at the impingement point for the modified design with radial jet and longer upper-lip is 29.1% higher than the original design at the same conditions. Besides, increasing the air-ring upper-lip height increased the averaged HTC, which is 13.4% higher than the original design.

Investigation of Heat Transfer for Shell-Tube Fuel-Cooled Heat Exchanger

2013 ◽  
Vol 378 ◽  
pp. 459-465
Author(s):  
Ya Guo Lu ◽  
Peng Fei Zhu
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Relative Error ◽  
Absolute Error ◽  
Heat Transfer Characteristics ◽  
Shell Side ◽  
Transfer Characteristics ◽  
Aero Engine ◽  
The Absolute

A calculate method based on ε-NTU model for heat transfer characteristics of shell-tube fuel-cooled heat exchanger of aero-engine lubrication system was built. The heat convection coefficient was obtained by a dimensionless curve (Re~StPr2/3), which was detailed introduced as well. A case study was executed at last. The absolute error of the outlet lubrication of the tube side and the shell side between the value of calculation and experiment was less than ±10°C, and the relative error was less than 6.5%. The absolute error of the heat transferred between calculation and experiment was less than ±0.9kW, and the relative error was less than 7.4%. It indicates that the mothod is available for the investigation of heat transfer characteristics of shell-tube fuel-cooled heat exchanger.

scholarly journals Comparison of MODIS and AERONET derived aerosol optical depth over the Ganga Basin, India

2005 ◽  
Vol 23 (4) ◽  
pp. 1093-1101 ◽  
Author(s):  
S. N. Tripathi ◽  
Sagnik Dey ◽  
A. Chandel ◽  
S. Srivastava ◽  
Ramesh P. Singh ◽  
...  
Keyword(s):  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Time Window ◽  
Absolute Error ◽  
Absolute Difference ◽  
Ganga Basin ◽  
Monsoon Period ◽  
Post Monsoon ◽  
Dust Loading ◽  
The Absolute

Abstract. The Moderate Resolution Imaging Spectroradiometer (MODIS) onboard EOS Terra measures global aerosol optical depth and optical properties since 2000. MODIS aerosol products are freely available and are being used for numerous studies. In this paper, we present a comparison of aerosol optical depth (AOD) retrieved from MODIS with Aerosol Robotic Network (AERONET) data for the year 2004 over Kanpur, an industrial city lying in the Ganga Basin in the northern part of India. AOD retrieved from MODIS (τaMODIS) at 0.55µm wavelength has been compared with the AERONET derived AOD (τaAERONET), within an optimum space-time window. Although the correlation between τaMODIS and τaAERONET during the post-monsoon and winter seasons (R2~0.71) is almost equal to that during the pre-monsoon and monsoon seasons (R2~0.72), MODIS is found to overestimate AOD during the pre-monsoon and monsoon period (characterized by severe dust loading) and underestimate during the post-monsoon and winter seasons. The absolute difference between τaMODIS and τaAERONET is found to be low (0.12±0.11) during the non-dust loading season and much higher (0.4±0.2) during dust-loading seasons. The absolute error in τaMODIS is found to be about ~25% of the absolute values of τaMODIS. Our comparison shows the importance of modifying the existing MODIS algorithm during the dust-loading seasons, especially in the Ganga Basin in northern part of India.

scholarly journals Intraocular Lens Power Calculation According to the Difference between Anterior and Total Keratometry Using Scheimpflug Imaging

2021 ◽  
Vol 62 (9) ◽  
pp. 1181-1188
Author(s):  
Joong Hee Kim ◽  
Kyong Jin Cho ◽  
Ho Seok Chung
Keyword(s):  
Regression Analysis ◽  
Absolute Error ◽  
Power Calculation ◽  
Intraocular Lens Power Calculation ◽  
Refractive Power ◽  
Simple Regression Analysis ◽  
The Absolute ◽  
The Difference ◽  
Lens Power ◽  
Simple Regression

Purpose: We investigated the change in the absolute error according to the difference between anterior and total keratometry, to determine the criterion for the difference in keratometry, and to determine the indication for using total keratometry. Methods: Sagittal and total refractive power were measured with 2-, 3-, and 4-mm Pentacam® rings, and the absolute error of each was calculated in patients who underwent cataract surgery in our hospital. The correlation between the difference value the sagittal minus the total refractive power and each absolute error was analyzed by simple regression analysis. The analysis was performed by dividing the patients into two groups based on 0.6, which is the average of the difference between the sagittal and total refractive power for the 3-mm ring. Results: Sagittal power was larger than total refractive power for all rings and the absolute error obtained by applying the total refractive power was larger than the sagittal power for the 2- and 4-mm rings (p < 0.001). The simple regression analysis revealed that the absolute error using sagittal power was positively correlated with the difference between sagittal power and total refractive power. In the group with less than 0.6, the absolute error using the total refractive power of all rings was larger than the sagittal power (p < 0.001). In the group exceeding 0.6, the absolute error using the total refractive power was less than using the sagittal power for the 3 mm ring (p = 0.028). Conclusions: The greater the difference between sagittal and total refractive power, the greater the absolute error using sagittal power. Accuracy was higher in the group exceeding 0.6 after applying total refractive power measured at the 3 mm ring compared to sagittal power.

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

Hydrodynamic Pressure of Thrust Step Bearings

2009 ◽  
Author(s):  
Shuangbiao Liu ◽  
W. Wayne Chen ◽  
Diann Y. Hua
Keyword(s):  
Analytical Solution ◽  
Coordinate System ◽  
Laplace Equation ◽  
Analytical Solutions ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Hydrodynamic Pressure ◽  
Finite Width ◽  
Cylindrical Coordinate ◽  
Lubrication Models

Step bearings are frequently used in industry for better load capacity. Analytical solutions to the Rayleigh step bearing and a rectangular slider with a finite width are available in literature, but none for a fan-shaped thrust step bearing. This study starts with a known solution to the Laplace equation in a cylindrical coordinate system, which is in the form of infinite summation. An analytical solution to pressure is derived in this paper for hydrodynamic lubrication problems encountered in the fan-shaped step bearing. The presented solutions can be useful for designers to maximize bearing performance as well as for researchers to benchmark numerical lubrication models.

scholarly journals FMCW Laser Fuze Multiple Scattering Model and Accurate Fixed-Distance Algorithm in a Smoke Environment

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2604
Author(s):  
Chengtian Song ◽  
Ying Cui ◽  
Bohu Liu
Keyword(s):  
Spectral Density ◽  
Multiple Scattering ◽  
Continuous Wave ◽  
Absolute Error ◽  
Suspended Particles ◽  
Scattering Model ◽  
Fixed Distance ◽  
The Absolute

In a smoke environment, suspended particles can scatter and absorb laser photons, making target echo signals extremely weak and difficult to extract and identify, which causes obvious difficulty in fixed-distance of laser fuze. In this paper, the multiple scattering model of frequency-modulated-continuous-wave (FMCW) laser fuze in a smoke environment was established. This model simulates multi-path propagation and multiple scattering of photons. At the same time, we use the correntropy spectral density (CSD) algorithm for accurate fixed-distance of FMCW laser fuze. The absolute error of distance does not exceed 0.15 m in smoke interference environment.

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