Meshless Local Petrov–Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

Dehghan, Mehdi; Mirzaei, Davoud

doi:10.1016/j.apnum.2008.05.001

Cited by 127 publications

(51 citation statements)

References 41 publications

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“…In order to avoid these oscillations the nodal distribution is again regular, with an aspect ratio 2:1, however, since the boundary layers are formed at x = 1and x = −1. The numerical results are compared with those obtained using the local boundary integral method (LBIE) [27] and the meshless-local PetrovGalerkin (MLPG) method [28]. The comparison reveals that, as time increases the numerical solutions of the proposed scheme for the velocity and the induced magnetic field tend to the exact solution of the steady state problem [3].…”

Section: Unsteady Mhd Flow In a Rectangular Duct With Insulating Or Cmentioning

confidence: 95%

“…In this way, it is possible the comparison of the present results with corresponding results of Figs. 2 and 3, obtained with MLPG method in [28]. Simultaneously, we can see how the Hartmann number and the conductivity parameter λ, affect the transition time to the steady state.…”

Section: Case 2: Conducting Wallsmentioning

confidence: 95%

“…Authors in [27] used the local boundary integral equation (LBIE) meshless method to obtain the numerical solution of the coupled equations for the velocity and the magnetic field for unsteady MHD flow through a pipe of rectangular and circular sections with nonconducting walls for low Hartmann numbers up to M = 40. The MLPG method was used in [28] for the numerical solution of the coupled equations in velocity and magnetic field for unsteady MHD flow through a pipe of rectangular section having arbitrary conducting walls. Results were presented for different Hartmann numbers up to 40. As it is refereed in [29], hitherto, there has been less research devoted to MFree strong-form methods, compared to weak-form descriptions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

et al. 2010

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In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 10 5 ) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local PetrovGalerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ∞ , the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.

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Section: Unsteady Mhd Flow In a Rectangular Duct With Insulating Or Cmentioning

confidence: 95%

Section: Case 2: Conducting Wallsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

et al. 2010

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“…Many of these methods employ basis functions obtained by the moving least-squares (MLS) technique but, except the collocation methods, the requirement of background cells for integration makes other methods (methods based on weak forms) not truly meshless methods. Meshless local boundary integral equation method [22][23][24][25] and meshless local PetrovGalerkin (MLPG) method [26][27][28][29][30][31][32][33][34][35][36][37] are two meshfree methods based on weak form which are truly meshless methods and so do not require background cells for numerical integration. This is the main advantage of these method, specially MLPG which its integrals are regular in spite of meshless LBIE.…”

mentioning

confidence: 99%

MLPG approximation to the p-Laplace problem

Mirzaei

Dehghan

2010

Comput Mech

Self Cite

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Meshless local Petrov-Galerkin (MLPG) method is discussed for solving 2D, nonlinear, elliptic p-Laplace or p-harmonic equation in this article. The problem is transferred to corresponding local boundary integral equation (LBIE) using Divergence theorem. The analyzed domain is divided into small circular sub-domains to which the LBIE is applied. To approximate the unknown physical quantities, nodal points spread over the analyzed domain and MLS approximation, are utilized. The method is a meshless method, since it does not require any background interpolation and integration cells and it dose not depend on geometry of domain. The proposed scheme is simple and computationally attractive. Applications are demonstrated through illustrative examples.

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“…For example Kadalbajoo and Sharma [5][6][7][8], Kadalbajoo and Ramesh [9], Amiraliyeva and Erdogan [10], Amiraliyeva and Amiraliyev [11], Rao and Chakravarthy [12] developed robust numerical schemes for dealing with singularly perturbed differential-difference equations. In recent years, much interest of scientists and engineeres has been paid on meshless based methods, particularly moving least squares (MLS) method [13][14][15][16][17]. In this paper, we employ a numerical method based on the MLS method to approximate the unknown function for solution of singularly perturbed differential-difference equations.…”

Section: Introductionmentioning

confidence: 99%

The numerical solution of the singularly perturbed differential-difference equations based on the Meshless method

Nadjafi

Ghassabzade

2014

International Journal of Applied Mathematical Research

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In this paper, we describe a meshless approach to solve singularly perturbed differential-difference equations of the second order with boundary layer at one end of the interval. In the numerical treatment for such type of problems, first we approximate the terms containing negative and positive shifts which converts it to a singularly perturbed differential equation. Next, a numerical scheme based on the moving least squares (MLS) method is used for solving singularly perturbed differential equation. The MLS methodology is a meshless method, because it does not need any background mesh or cell structures. The proposed scheme is simple and efficient to approximate the unknown function. Several examples are presented to demonstrate the efficiency and validity of the numerical scheme presented in the paper.

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Meshless Local Petrov–Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

Cited by 127 publications

References 41 publications

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

MLPG approximation to the p-Laplace problem

The numerical solution of the singularly perturbed differential-difference equations based on the Meshless method

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