Wavelet Lifting Scheme for the Numerical Solution of Dynamic Reynolds Equation for Micropolar Fluid Lubrication

2021 ◽  
pp. 2150033
Author(s):  
S. C. Shiralashetti ◽  
M. H. Kantli ◽  
A. B. Deshi
Keyword(s):  
Numerical Solution ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Lifting Scheme ◽  
Computational Time ◽  
Biorthogonal Wavelets ◽  
Wavelet Theory ◽  
Science And Engineering ◽  
Promising Tool ◽  
Wavelet Lifting

Recently, wavelet theory has become a well recognized promising tool in science and engineering field; especially, wavelets are successfully used in fast algorithms for easy execution. In this paper, we developed wavelet lifting scheme using orthogonal and biorthogonal wavelets for the numerical solution of dynamic Reynolds equation for micropolar fluid lubrication. The numerical results gained through proposed scheme are compared with the exact solution to expose the accuracy with speed of convergence in lesser computational time as compared with the existing methods. The examples are given to demonstrate the applicability and attractiveness of proposed method.

Wavelet-based lifting scheme for the numerical solution of some class of nonlinear partial differential equations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850046 ◽  
Author(s):  
S. C. Shiralashetti ◽  
L. M. Angadi ◽  
A. B. Deshi
Keyword(s):  
Numerical Solution ◽  
Nonlinear Partial Differential Equations ◽  
Lifting Scheme ◽  
Nonlinear Pdes ◽  
Computational Time ◽  
Test Problems ◽  
Wavelet Filter ◽  
Science And Engineering ◽  
Partial Differential ◽  
Physical Phenomena

Partial differential equation (PDE) occurs in the mathematical modeling of many physical phenomena arising in science and engineering. In this paper, we present wavelet-based lifting scheme for the numerical solution of nonlinear PDEs using different wavelet filter coefficients. The numerical results obtained by this scheme are compared with the exact solution to demonstrate the accuracy and also speeds up convergence in lesser computational time as compared with the existing schemes. Some test problems are presented for the validity and applicability of the scheme.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR DYNAMIC EQUATION OF UNDERWATER TOWED SYSTEM

2014 ◽  
Vol 11 (04) ◽  
pp. 1350060 ◽  
Author(s):  
ZHIJIANG YUAN ◽  
LIANGAN JIN ◽  
WEI CHI ◽  
HENGDOU TIAN
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Computational Time ◽  
Algebraic Equations ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

A wide body of work exists that describes numerical solution for the nonlinear system of underwater towed system. Many researchers usually divide the tow cable with less number elements for the consideration of computational time. However, this type of installation affects the accuracy of the numerical solution. In this paper, a newly finite difference method for solving the nonlinear dynamic equations of the towed system is developed. The mathematical model of tow cable and towed body are both discretized to nonlinear algebraic equations by center finite difference method. A newly discipline for formulating the nonlinear equations and Jacobian matrix of towed system are proposed. We can solve the nonlinear dynamic equation of underwater towed system quickly by using this discipline, when the size of number elements is large.

The Temporal Evolution of Particle Population Involving Simultaneous Coagulation, Diffusion Deposition, Gravity Sedimentation and Ventilation in the Fixed Space

2012 ◽  
Vol 516-517 ◽  
pp. 813-816
Author(s):  
Juan Fu ◽  
Zhi Ning ◽  
Yun Chao Song ◽  
Ming Lv
Keyword(s):  
Numerical Solution ◽  
Dynamic Behavior ◽  
Balance Equation ◽  
Temporal Evolution ◽  
Population Balance Equation ◽  
Small Particles ◽  
Science And Engineering ◽  
Particle Population ◽  
Fixed Space ◽  
Gravity Sedimentation

The dynamic behavior of small particles in fixed spaces is of interest in various fields of science and engineering. In the paper, a population balance equation for particles in fixed space is established to describe the dynamic behavior of system involving simultaneous coagulation, diffusion deposition, gravity sedimentation and ventilation. Related Parameters are decided by experiments for the convenience of achieving numerical solution of the equation. Finally, the temporal evolution of particles population in fixed space is simulated and discussed under different conditions.

Relative time seislet transform

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V223-V232 ◽  
Author(s):  
Zhicheng Geng ◽  
Xinming Wu ◽  
Sergey Fomel ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Lifting Scheme ◽  
Real Data ◽  
Data Sets ◽  
Relative Time ◽  
New Approach ◽  
New Formulation ◽  
Wavelet Lifting ◽  
Seismic Images

The seislet transform uses the wavelet-lifting scheme and local slopes to analyze the seismic data. In its definition, the designing of prediction operators specifically for seismic images and data is an important issue. We have developed a new formulation of the seislet transform based on the relative time (RT) attribute. This method uses the RT volume to construct multiscale prediction operators. With the new prediction operators, the seislet transform gets accelerated because distant traces get predicted directly. We apply our method to synthetic and real data to demonstrate that the new approach reduces computational cost and obtains excellent sparse representation on test data sets.

A Hybrid Mobility Solution Method for Dynamically Loaded Misaligned Journal Bearings

2012 ◽  
Author(s):  
S. Boedo
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Solution Method ◽  
Hybrid Approach ◽  
Journal Bearings ◽  
Finite Element Solution ◽  
Computational Time ◽  
Element Solution ◽  
Dynamically Loaded ◽  
Mobility Solution

This paper presents a hybrid mobility solution approach to the analysis of dynamically loaded misaligned journal bearings. Mobility data obtained for misaligned bearings (calculated from a finite element representation of the Reynolds equation) are compared with existing curve-fitted mobility maps representative of a perfectly aligned bearing. A relative error analysis of mobility magnitude and direction provides a set of misaligned journal bearing configurations (midplane eccentricity ratio and normalized misalignment angle) where existing curve-fitted mobility map components based on aligned bearings can be used to calculate the resulting journal motion. For bearing configurations where these mobility maps are not applicable, the numerical simulation process proceeds using a complete finite element solution of the Reynolds equation. A set of numerical examples representing misaligned main and connecting rod bearings in a four-stroke automotive engine illustrate the hybrid solution method. Substantial savings in computational time are obtained using the hybrid approach over the complete finite element solution method without loss of computational accuracy.

A Hybrid Mobility Solution Approach for Dynamically Loaded Misaligned Journal Bearings

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
S. Boedo
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Solution Method ◽  
Journal Bearings ◽  
Finite Element Solution ◽  
Computational Time ◽  
Element Solution ◽  
Solution Approach ◽  
Dynamically Loaded ◽  
Mobility Solution

This paper presents a hybrid mobility solution approach to the analysis of dynamically loaded misaligned journal bearings. Mobility data obtained for misaligned bearings (calculated from a finite element representation of the Reynolds equation) are compared with existing curve-fitted mobility maps representative of a perfectly aligned bearing. A relative error analysis of mobility magnitude and direction provides a set of misaligned journal bearing configurations (midplane eccentricity ratio and normalized misalignment angle), where existing curve-fitted mobility map components based on aligned bearings can be used to calculate the resulting journal motion. For bearing configurations where these mobility maps are not applicable, the numerical simulation process proceeds using a complete finite element solution of the Reynolds equation. A numerical example representing a misaligned main bearing in a four-stroke automotive engine illustrates the hybrid solution method. Substantial savings in computational time are obtained using the hybrid approach over the complete finite element solution method without loss of computational accuracy.

Sign in / Sign up

Export Citation Format

Share Document