scholarly journals A Non-Standard Finite Difference Scheme for Magneto-Hydro Dynamics Boundary Layer Flows of an Incompressible Fluid Past a Flat Plate

2021 ◽  
Vol 26 (1) ◽  
pp. 22
Author(s):  
Riccardo Fazio ◽  
Alessandra Jannelli
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Flat Plate ◽  
Finite Difference Scheme ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Uniform Mesh ◽  
Wide Range

This paper deals with a non-standard implicit finite difference scheme that is defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. The proposed approach allows imposing the given boundary conditions at infinity exactly. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

scholarly journals A Non-Standard Finite Difference Scheme for Magneto-Hydro Dynamics Boundary Layer Flows of an Incompressible Fluid Past a Flat Plate

2021 ◽  
Author(s):  
Riccardo Fazio ◽  
Alessandra Jannelli
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Flat Plate ◽  
Finite Difference Scheme ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Uniform Mesh ◽  
Wide Range

This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

A parameter-uniform finite difference scheme for singularly perturbed parabolic problem with two small parameters

2021 ◽  
Author(s):  
Tesfaye Aga Bullo ◽  
Guy Aymard Degla ◽  
Gemechis File Duressa
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Variable Parameter ◽  
Accurate Solution ◽  
Singularly Perturbed ◽  
Finite Difference Approximation ◽  
Parabolic Problems ◽  
Difference Approximation ◽  
Uniform Mesh

A parameter-uniform finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with two parameters. The solution involves boundary layers at both the left and right ends of the solution domain. A numerical algorithm is formulated based on uniform mesh finite difference approximation for time variable and appropriate piecewise uniform mesh for the spatial variable. Parameter-uniform error bounds are established for both theoretical and experimental results and observed that the scheme is second-order convergent. Furthermore, the present method produces a more accurate solution than some methods existing in the literature.   

scholarly journals Stability Analysis of the Laminar Boundary Layer Flow

1970 ◽  
Vol 29 ◽  
pp. 23-34
Author(s):  
Nazma Parveen ◽  
Md MK Chowdhury
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Stability Analysis ◽  
Finite Difference ◽  
Difference Scheme ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Finite Difference Scheme ◽  
Linear Set ◽  
Layer Flow

In this paper, stability analysis of incompressible laminar boundary layer flow is presented. For this approach, the partial differential equation is converted to ordinary differential equation by suitable approximation. The implicit finite difference scheme is used to find the point of separations of the boundary layer equations. The finite difference equations for the given flow at each longitudinal position form a linear set with a tridiagonal coefficient matrix. To ensure the correct results, the methods are checked with standard flows like flow past circular cylinder, Howarth’s linear decelerating flows. These methods are demonstrated to compute accurately the separation points of several flows for which comparisons are made with previously published results. Then various series are tested with computer codes. At last, the stability diagram for plane poiseuille flow is shown. Key words: Stability; finite difference scheme; point of separation GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 23-34  DOI: http://dx.doi.org/10.3329/ganit.v29i0.8512

scholarly journals SCHEMES CONVERGENT Ε-UNIFORMLY FOR PARABOLIC SINGULARLY PERTURBED PROBLEMS WITH A DEGENERATING CONVECTIVE TERM AND A DISCONTINUOUS SOURCE

2015 ◽  
Vol 20 (5) ◽  
pp. 641-657 ◽  
Author(s):  
Carmelo Clavero ◽  
Jose Luis Gracia ◽  
Grigorii I. Shishkin ◽  
Lidia P. Shishkina
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Euler Method ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Interior Layer ◽  
Convective Term ◽  
Singularly Perturbed Problems ◽  
First Order

We consider the numerical approximation of a 1D singularly perturbed convection-diffusion problem with a multiply degenerating convective term, for which the order of degeneracy is 2p + 1, p is an integer with p ≥ 1, and such that the convective flux is directed into the domain. The solution exhibits an interior layer at the degeneration point if the source term is also a discontinuous function at this point. We give appropriate bounds for the derivatives of the exact solution of the continuous problem, showing its asymptotic behavior with respect to the perturbation parameter ε, which is the diffusion coefficient. We construct a monotone finite difference scheme combining the implicit Euler method, on a uniform mesh, to discretize in time, and the upwind finite difference scheme, constructed on a piecewise uniform Shishkin mesh condensing in a neighborhood of the interior layer region, to discretize in space. We prove that the method is convergent uniformly with respect to the parameter ε, i.e., ε-uniformly convergent, having first order convergence in time and almost first order in space. Some numerical results corroborating the theoretical results are showed.

scholarly journals An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Canan Koroglu ◽  
Ayhan Aydin
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Truncation Error ◽  
Vries Equation ◽  
Mkdv Equation ◽  
Numerical Results ◽  
De Vries ◽  
Nsfd Scheme ◽  
Theta Method

A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.

MHD flows on irregular boundary over a diverging channel with viscous dissipation effect

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Iyyappan G. ◽  
Abhishek Kumar Singh
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Difference Scheme ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Finite Difference Scheme ◽  
Uniform Mesh ◽  
Irregular Boundary ◽  
Content Type ◽  
Diverging Channel

Purpose The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur. Design/methodology/approach The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh. Findings The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2. Originality/value The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

scholarly journals DIFFERENCE SCHEME FOR DYNAMIC SIMULATION DESCRIBING STOCHASTIC KINETICS OF MOLECULES IN CERAMICS

1998 ◽  
Vol 3 (1) ◽  
pp. 93-97
Author(s):  
V. Frishfelds ◽  
I. Madzhulis ◽  
J. Rimshans
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Dynamic Simulation ◽  
Finite Difference Scheme ◽  
Numerical Results ◽  
Computational Experiments ◽  
Kinetics Of ◽  
Stochastic Kinetics

A conservative and monotonous finite difference scheme is proposed for solving PDE describing the kinetics of molecules in ceramics. Numerical results of computational experiments are presented.

scholarly journals Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekar Elango ◽  
Ayyadurai Tamilselvan ◽  
R. Vadivel ◽  
Nallappan Gunasekaran ◽  
Haitao Zhu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Boundary Layers ◽  
Finite Difference Scheme ◽  
Nonlocal Boundary ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Integral Boundary ◽  
Delay Term

AbstractThis paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain. A numerical method comprising the standard finite difference scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of $N_{r} \times N_{t}$ N r × N t elements condensing in the boundary layers is suggested, and it is proved to be parameter-uniform. Also, the order of convergence is proved to be almost two in space variable and almost one in time variable. Numerical examples are proposed to validate the theory.

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