scholarly journals Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Hossein Aminikhah ◽  
Somayyeh Kazemi
Keyword(s):  
Boundary Layer ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Method ◽  
Flow Problem ◽  
Spline Method ◽  
B Spline ◽  
Theoretical Considerations ◽  
Uniform Stream

A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error L2-norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

The boundary layer in crossed-fields m.h.d.

1966 ◽  
Vol 25 (2) ◽  
pp. 229-240 ◽  
Author(s):  
W. R. Sears
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Plate ◽  
Flow Problem ◽  
Inviscid Flow ◽  
Magnetic Reynolds Number ◽  
Large Reynolds Number ◽  
Zero Values ◽  
Plate Solution ◽  
A Current

This study of the boundary layer of steady, incompressible, plane, crossed-fields m.h.d. flow at large Reynolds numberReand magnetic Reynolds numberRmbegins with a review of Hartmann's case, where a boundary layer occurs whose thickness is proportional to (Re Rm)−½. Following this clue, it is shown that in general the boundary layer is a ‘local Hartmann boundary layer’. Its profiles are always exponential and it is determined completely by local quantities. The skin friction and the total electric current in the layer are proportional to the square root of the magnetic Prandtl number, i.e. to (Rm/Re)½. Thus the exterior-flow problem, the solution of which precedes a boundary-layer solution, generally involves a current sheet at the fluid-solid interface.This inviscid-flow problem becomes tractable if (Rm/Re)½is small enough to permit a linearized solution. The flow field about a flat plate at zero incidence is calculated in this approximation. It is pointed out that the thin-cylinder solutions of Sears & Resler (1959), which pertain toRm/Re= 0, can immediately be extended to small, non-zero values of this parameter by linear combination with this flat-plate solution.

The effect of buoyancy forces on the boundary-layer flow over a semi-infinite vertical flat plate in a uniform free stream

1969 ◽  
Vol 35 (3) ◽  
pp. 439-450 ◽  
Author(s):  
J. H. Merkin
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Method ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Leading Edge ◽  
Series Solutions ◽  
Buoyancy Forces ◽  
Layer Flow ◽  
Vertical Flat Plate

The boundary-layer flow over a semi-infinite vertical flat plate, heated to a constant temperature in a uniform free stream, is discussed in the two cases when the buoyancy forces aid and oppose the development of the boundary layer. In the former case, two series solutions are obtained, one of which is valid near the leading edge and the other is valid asymptotically. An accurate numerical method is used to describe the flow in the region where the series are not valid. In the latter case, a series, valid near the leading edge is obtained and it is extended by a numerical method to the point where the boundary layer is shown to separate.

On the numerical solution of the nonlinear Bratu type equation via quintic B-spline method

2019 ◽  
Vol 22 (4) ◽  
pp. 405-413 ◽  
Author(s):  
Osama Ala’yed ◽  
Belal Batiha ◽  
Raft Abdelrahim ◽  
Ala’a Jawarneh
Keyword(s):  
Numerical Solution ◽  
Type Equation ◽  
Spline Method ◽  
B Spline
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