scholarly journals Numerical Method in Two Dimensional Boundary Layer Theory for Incompressible Viscous Fluid

2013 ◽  
Vol 38 ◽  
pp. 61-73
Author(s):  
MA Haque
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Initial Value Problem ◽  
Shooting Method ◽  
Boundary Layer Equation ◽  
Incompressible Viscous Fluid ◽  
Initial Value ◽  
Box Scheme ◽  
Runge Kutta Method ◽  
Dimensional Boundary

In this paper laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) Shooting Method. In Shooting Method, the boundary value problem has been converted into an equivalent initial value problem. Finally the Runge-Kutta method is used to solve the initial value problem. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16549 Rajshahi University J. of Sci. 38, 61-73 (2010)

An Initial Value Method for the Solution of a Class of Nonlinear Equations in Fluid Mechanics

1970 ◽  
Vol 92 (3) ◽  
pp. 503-508 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Porous Medium ◽  
Fluid Mechanics ◽  
Boundary Layer Equation ◽  
Physical Parameters ◽  
Point Boundary ◽  
Trial And Error ◽  
Initial Value ◽  
Blasius Boundary Layer

An initial value method is introduced in this paper for the solution of a class of nonlinear two-point boundary value problems. The method can be applied to the class of equations where certain physical parameters appear either in the differential equation or in the boundary conditions or both. Application of this method to two problems in Fluid Mechanics, namely, Blasius’ boundary layer equation with suction (or blowing) and/or slip and the unsteady flow of a gas through a porous medium, are presented as illustrations of this method. The trial-and-error process usually required for the solution of such equations is eliminated.

Modeling of the Convective Thermal Ignition Process of Solid Fuel Particles

1990 ◽  
Vol 112 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
Jing-Tang Yang ◽  
Gwo-Guang Wang ◽  
Hung-Yi Li
Keyword(s):  
Boundary Layer ◽  
Gas Phase ◽  
Azimuthal Angle ◽  
Ignition Process ◽  
Thermal Ignition ◽  
Boundary Layer Equations ◽  
Runge Kutta Method ◽  
Convective Thermal ◽  
Dimensional Boundary ◽  
Fuel Particles

This work uses the boundary layer theory to study the thermal ignition process of the solid particle. The theoretical model explores the two-dimensional boundary layer equations in the gaseous phase. The governing equations of mass, momentum, energy, and species in gas phase are first transformed to ordinary differential equations through series expansion with respect to the azimuthal angle. The equations are then quasi-linearized to be the initial value problem and solved using Runge-Kutta method. The minimum heat flux from the gas phase to the fuel is evaluated as the most suitable criterion for the convective thermal ignition. The influences of the heat transfer rate, fluid dynamics, and the gas phase chemical reaction rate on the ignition delay and ignition position are discussed in detail.

Numerical treatment of a quasilinear initial value problem with boundary layer

2015 ◽  
Vol 93 (11) ◽  
pp. 1845-1859
Author(s):  
Musa Cakir ◽  
Erkan Cimen ◽  
Ilhame Amirali ◽  
Gabil M. Amiraliyev
Keyword(s):  
Boundary Layer ◽  
Initial Value Problem ◽  
Numerical Treatment ◽  
Initial Value

A New Efficient Ode Solver For Solving Initial Value Problem

1998 ◽  
pp. 47-56
Author(s):  
Nazeeruddin Yaacob ◽  
Bahrom Sanugi
Keyword(s):  
Stability Analysis ◽  
Explicit Formula ◽  
Fourth Order ◽  
Initial Value Problem ◽  
Harmonic Mean ◽  
Kutta Method ◽  
Initial Value ◽  
Order Accuracy ◽  
Runge Kutta Method ◽  
Runge Kutta

In this paper we develop a new three-stage,fourth order explicit formula of Runge-Kutta type based on Arithmetic and Harmonic means.The error and stability analyses of this method indicate that the method is stable and efficient for nonstiff problems.Two examples are given which illustrate the fcurth order accuracy of the method. Keywords: Runge-Kutta method, Harmonic Mean, three-stage, fourth-order, covergence and stability analysis.

Numerical Solution of the Flow Between Two Disks

1997 ◽  
Author(s):  
Wahid S. Ghaly ◽  
Georgios H. Vatistas
Keyword(s):  
Shooting Method ◽  
Static Pressure ◽  
Numerical Solutions ◽  
Kutta Method ◽  
Initial Value ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
First Order ◽  
Pressure Distributions ◽  
Runge Kutta Method

Abstract This paper deals with the numerical solutions of converging and diverging flows, between two disks. The results are obtained by solving a nonlinear third order ordinary differential equation using a modified shooting method. The governing equation is written as a system of three nonlinear first order ODE’s and the resulting system is solved as an initial value problem via the Runge-Kutta method. The results are given in terms of velocity profiles and static pressure distributions. These are compared with previously reported experimental data obtained by others.

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