Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

Non-Linear Static Analysis of 2D Steep Wave Riser Under Current Load

2016 ◽  
Author(s):  
Hongdong Qiao ◽  
Weidong Ruan ◽  
Zhaohui Shang ◽  
Yong Bai
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Shooting Method ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Steep Wave

A new solution combining finite difference method and shooting method is developed to analyze the behavior of steep wave riser subjected to current loading. Based on the large deformation beam theory and mechanics equilibrium principle, a set of non-linear ordinary differential equations describing the motion of the steep wave riser are obtained. Then, finite difference method and shooting method are adopted and combined to solve the ordinary differential equations with zero moment boundary conditions at both the seabed end and surface end of the steep wave riser. The resulting non-linear finite difference formulations can be solved effectively by Newton-Raphson method. To improve iterative efficiency, shooting method is also employed to obtain the initial value for Newton-Raphson method. Results are compared with that of FEM by OrcaFlex, to verify the accuracy and reliability of the numerical method. Finally, a series of sensitivity analyses are also performed to highlight the influencing parameters in the steep wave riser.

Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem

2003 ◽  
Vol 125 (3) ◽  
pp. 523-527 ◽  
Author(s):  
James Caldwell ◽  
Svetislav Savovic´ ◽  
Yuen-Yick Kwan
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Finite Difference Methods ◽  
Melting Process ◽  
Time Dependent ◽  
One Dimensional ◽  
Stefan Problems ◽  
Finite Difference Solution ◽  
Very High

The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process. However, very few explicit analytical solutions are available in the literature for such problems, particularly with time-dependent boundary conditions. Benchmark cases are presented involving two test examples with the aim of producing very high accuracy when validated against the exact solutions. Test example 1 (time-independent boundary conditions) is followed by the more difficult test example 2 (time-dependent boundary conditions). As a result, the temperature distribution, position of the moving boundary and the velocity are evaluated and the results are validated.

The Numerical Solution of Linear Elliptic Equations

1968 ◽  
Vol 90 (4) ◽  
pp. 773-776 ◽  
Author(s):  
R. Coleman
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Difference Method ◽  
Elliptic Equations ◽  
Linear Boundary ◽  
Numerical Techniques ◽  
Spiral Groove ◽  
Gas Bearing

A noniterative finite difference method is given for the solutions of linear elliptic equations with linear boundary conditions. This method is applicable to a variety of gas bearing problems. Comparisons are made with other numerical techniques, and an application to the spiral groove thrust plate is given.

scholarly journals A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Sanaullah Jamali
Keyword(s):  
Numerical Analysis ◽  
Numerical Solution ◽  
Bisection Method ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Derivative Free Method ◽  
Newton Raphson ◽  
Transcendental Equations ◽  
Regula Falsi Method ◽  
Raphson Method

Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist in literature to find roots but in this paper, we introduce a unique idea by using the interpolation technique. The proposed method derived from the newton backward interpolation technique and the convergence of the proposed method is quadratic, all types of problems (taken from literature) have been solved by this method and compared their results with another existing method (bisection method (BM), regula falsi method (RFM), secant method (SM) and newton raphson method (NRM)) it’s observed that the proposed method have fast convergence. MATLAB/C++ software is used to solve problems by different methods.

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