Numerical solutions of the one-phase classical Stefan problem using an enthalpy green element formulation

Onyejekwe, Okey Oseloka; Onyejekwe, Ogugua

doi:10.1016/j.advengsoft.2011.05.012

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…Such a transformation will give a false sense of accuracy, because the rigor incurred in order to achieve a BEM domain-reduction is more often than not compensated for by accuracy. The second point is that by dealing directly with such problems without an undue resort to approximations and by discretizing the problem domain we open the door for handling problems involving heterogeneity and nonlinearity (Onyejekwe and Onyejekwe [18], Onyejekwe [19]). The overall significance of our investigation is that it opens the chapter on the development of highly accurate hybrid boundary integral numerical algorithms for boundary layer flows involving similarity transformations.…”

Section: Resultsmentioning

confidence: 99%

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

Onyejekwe¹

2016

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This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate according to the approximations resulting from Prandtl boundary layer theory. The governing nonlinear coupled partial differential equations describing laminar flow are converted to a self-similar type third order ordinary differential equation known as the Falkner-Skan equation. For the purposes of a numerical solution, the Falkner-Skan equation is converted to a system of first order ordinary differential equations. These are numerically addressed by the conventional shooting and bisection methods coupled with the Runge-Kutta technique. However the accompanying energy equation lends itself to a hybrid numerical finite element-boundary integral application. An appropriate complementary differential equation as well as the Green second identity paves the way for the integral representation of the energy equation. This is followed by a finite element-type discretization of the problem domain. Based on the quality of the results obtained herein, a strong case is made for a hybrid numerical scheme as a useful approach for the numerical resolution of boundary layer flows and species transport. Thanks to the sparsity of the resulting coefficient matrix, the solution profiles not only agree with those of similar problems in literature but also are in consonance with the physics they represent.

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Section: Resultsmentioning

confidence: 99%

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

Onyejekwe¹

2016

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“…The compelling need to make BEM a purely boundary-driven numerical technique motivates this trend. Unfortunately this is often accompanied by some numerical challenges some of which have been mentioned above and in some previous papers (Percher et al [26], Lorinczi [27], Lorinczi et al [28], Archer et al [29], Archer [30], Onyejekwe [31,32], Onyejekwe and Onyejekwe [33] Archer and Horne [34]). Numerical experience shows that direct application of BEM theory performs poorly in the absence of a strong link between the problem domain and the boundary as is found in the Laplace equation.…”

Section: Introductionmentioning

confidence: 99%

An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

Onyejekwe¹

2017

IJFMTS

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Abstract:To further improve on the competitiveness of the boundary element method (BEM), a hybrid version of it is used for a numerical solution of two dimensional nonlinear coupled viscous Burger's equation. Adopting this approach to a discretized 2D spatial domain, the resulting integral equations arising from the singular integral theory are applied locally to each of the elements. The resulting nonlinear discrete equations are finally solved by the Picard iteration algorithm. The simulation results obtained, not only concur with analytical solutions, but also display high accuracy and are in agreement with those available in literature.

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“…With the advent of computers and sophisticated solution methods, numerical and approximate analytical techniques are now employed to solve different types of Stefan problems. Some of these methods include finite difference method [16]- [17], green element method [6], variable space grid [9]- [10],boundary immobilization schemes [8]- [10], adomain decomposition method [6]- [7], heat balance integral method [12],homotopy perturbation method [3], variation iteration method [5] and variable space grid [15]. In paper [4], Jafari et al used HAM to solve the Stefan problem with Dirichlet boundary conditions and no forcing term.…”

Section: Introductionmentioning

confidence: 99%

The solution of a one-phase Stefan problem with a forcing term by homotopy analysis method

Onyejekwe

2014

International Journal of Advanced Mathematical Sciences

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In this paper, we use the homotopy analysis method (HAM), to obtain the solutions of the temperature distribution, the position of the moving boundary and the Stefan condition. There are advantages to using HAM, firstly it is independent of small/large physical parameters, there is flexibility on the choice of base function and initial guess of solution and lastly there is great generality. The results obtained from this method shows high accuracy, computational efficiency and a strong rate of convergence.

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Numerical solutions of the one-phase classical Stefan problem using an enthalpy green element formulation

Cited by 6 publications

References 17 publications

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

An Element-Driven Boundary Integral Treatment for Nonlinearity: A Coupled Nonlinear Two-Dimensional Burger’s Equation Test Case

The solution of a one-phase Stefan problem with a forcing term by homotopy analysis method

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