scholarly journals The method of numerical solution of the one stationary hydrodynamics problem in convective form in $L$-shaped domain

2020 ◽  
Vol 12 (6) ◽  
pp. 1291-1306
Author(s):  
Viktor A Rukavishnikov ◽  
Alexey Viktorovich Rukavishnikov
Keyword(s):  
Numerical Solution ◽  
The One ◽  
Shaped Domain

Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

2018 ◽  
Vol 284 ◽  
pp. 1230-1234
Author(s):  
Mikhail V. Maisuradze ◽  
Alexandra A. Kuklina
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Differential Diffusion ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Diffusion ◽  
Simplified Algorithm ◽  
The One ◽  
Carburizing Process ◽  
Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

scholarly journals Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

2015 ◽  
Vol 62 (3-4) ◽  
pp. 101-119 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Dzmitry Prybytak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Cross Sections ◽  
Flow Model ◽  
One Dimensional ◽  
Averaging Methods ◽  
Integration Formulas ◽  
Different Types ◽  
The One

AbstractIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

scholarly journals ENERGY-CONSERVING AND RECIPROCAL SOLUTIONS FOR HIGHER-ORDER PARABOLIC EQUATIONS

2001 ◽  
Vol 09 (01) ◽  
pp. 183-203 ◽  
Author(s):  
DMITRY MIKHIN
Keyword(s):  
Finite Difference ◽  
Energy Conservation ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Finite Difference Scheme ◽  
Flow Reversal ◽  
Difference Operators ◽  
Energy Conserving ◽  
The One ◽  
Moving Media

The energy conservation law and the flow reversal theorem are valid for underwater acoustic fields. In media at rest the theorem transforms into well-known reciprocity principle. The presented parabolic equation (PE) model strictly preserves these important physical properties in the numerical solution. The new PE is obtained from the one-way wave equation by Godin12 via Padé approximation of the square root operator and generalized to the case of moving media. The PE is range-dependent and explicitly includes range derivatives of the medium parameters. Implicit finite difference scheme solves the PE written in terms of energy flux. Such formalism inherently provides simple and exact energy-conserving boundary condition at vertical interfaces. The finite-difference operators, the discreet boundary conditions, and the self-starter are derived by discretization of the differential PE. Discreet energy conservation and flow reversal theorem are rigorously proved as mathematical properties of the finite-difference scheme and confirmed by numerical modeling. Numerical solution is shown to be reciprocal with accuracy of 10–12 decimal digits, which is the accuracy of round-off errors. Energy conservation and wide-angle capabilities of the model are illustrated by comparison with two-way normal mode solutions including the ASA benchmark wedge.

The Equation of the Limit Replacement Width of Non-Newton Fluid in Eccentric Annulus

2013 ◽  
Vol 807-809 ◽  
pp. 2616-2619
Author(s):  
Yin Qing Liu ◽  
Mei Wei Wang ◽  
Hai Qing Cui
Keyword(s):  
Numerical Solution ◽  
Rheological Properties ◽  
Power Law ◽  
Solution Method ◽  
Cement Slurry ◽  
Power Law Fluid ◽  
Two Phase ◽  
Numerical Solution Method ◽  
Eccentric Annulus ◽  
The One

The equation of the limit replacement width of the one-dimension two-phase flow of Bingham fluid replacing Power law fluid in eccentric annulus was established, the numerical solution method of the equation mentioned above was given and taking the 3 wells, such as the He 104-27 well etc for examples, the limit replacement widths of cement slurry displacing mud, whose rheological properties can be described as Bingham and Power law modles respectively, were calculated, by using the equation and the numerical solution method mentioned above, and compared with those of cement slurry displacing mud, whose rheological properties are all described as Binghanm modle.

Sign in / Sign up

Export Citation Format

Share Document