Linearized-Boltzmann-type-equation-based finite difference method for thermal incompressible flow

2012 ◽  
Vol 69 ◽  
pp. 67-80 ◽  
Author(s):  
S.C. Fu ◽  
R.M.C. So ◽  
W.W.F. Leung
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Incompressible Flow ◽  
Difference Method ◽  
Type Equation

scholarly journals the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes

2021 ◽  
Vol 1 (1) ◽  
pp. 18-23
Author(s):  
Pramod Pandey
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Boundary Value ◽  
Type Equation ◽  
Step Length ◽  
Computational Results ◽  
Order Of Accuracy ◽  
Variable Step

In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate.

ANALYSIS OF THE VALUES OF HYDRODYNAMIC PRESSURE AND LOAD CARRYING CAPACITIES FOR VARIOUS METHODS OF SOLVING A REYNOLDS TYPE EQUATION

Tribologia ◽  
2018 ◽  
Vol 280 (4) ◽  
pp. 55-62
Author(s):  
Andrzej MISZCZAK ◽  
Krzysztof WIERZCHOLSKI
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Type Equation ◽  
Hydrodynamic Pressure ◽  
Viscosity Change ◽  
Slide Bearing ◽  
The Finite Difference Method ◽  
Viscosity Changes ◽  
Calculation Procedures

Calculations of the hydrodynamic pressure distribution in the slide bearing gap occur most often on the basis of ready-made computer programs based on CFD methods or one’s own calculation procedures based on various numerical methods. The use of one’s own calculation procedures and, for example, the finite difference method, allows one to include in the calculations of various additional non-classical effects on the lubricant (e.g., the influence of the magnetic field on ferrofluid, the influence of pressure or temperature on viscosity changes, non-Newtonian properties of lubricant or various non-classical models of dynamic viscosity changes). The aim of the authors’ research is to check how large the differences in results may be obtained using the two most frequently used methods of solving a Reynolds type equation. In this work, the authors use the small parameter method and the method of subsequent approximations to determine the distribution of hydrodynamic pressure. For numerical calculations, the finite difference method and our own calculation procedures and Mathcad 15 software were used. With both methods, identical conditions and parameters were assumed and the influence of pressure and temperature on viscosity change was taken into account. In the hydrodynamic pressure calculations, a laminar flow of the lubricating liquid and a non-isothermal lubrication model of the slide bearing were adopted. The classic Newtonian model was used as a constitutive equation. A cylindrical-type slide bearing of finite length with a smooth pan with a full wrap angle was accepted for consideration. In the thin layer of the oil film, the density and thermal conduction coefficient of the oil were assumed to remain unchanged.

HEAT TRANSFER IN LARGE RUBBER ELEMENTS THROUGH OF MODELING BY FINITE DIFFERENCE METHOD

2019 ◽  
Author(s):  
Lucas Peixoto ◽  
Ane Lis Marocki ◽  
Celso Vieira Junior ◽  
Viviana Mariani
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

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