Simulation of laminar backward facing step flow under magnetic field with explicit local radial basis function collocation method

Mramor, Katarina; Vertnik, Robert; Šarler, Božidar

doi:10.1016/j.enganabound.2014.04.013

Cited by 35 publications

(33 citation statements)

References 41 publications

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“…At the end of the channel, the velocity profile recovers to the Hartmann flow. The present u −velocity profiles at Ha =10 are compared with the results of Mramor et al and Granados et al in Figure . Although the velocity profiles are very similar, there is some difference for the velocity profile at x =2 in Figure A.…”

Section: Numerical Resultsmentioning

confidence: 75%

“…The numerical simulation of two‐dimensional incompressible flow over a backward facing step with an expansion ratio (outlet to inlet height) of two has been the classical benchmark problem for separated flows . The present validation case corresponds to the incompressible flow of an electrically conducting fluid inside a channel with a backward facing step considered by Mramor et al and Granados et al The computational domain consists of (−2,15)×(0,1)∖(−2,0]×(0,0.5]. Therefore, the maximum channel height H is unity.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The comparison of computed velocity profiles with the results of the works of Mramor et al and Granados et al at x =2 (A), x =7 (B), and x =15 (C) for R e =800, R e m =1, and N =1.25×10 −1 ( H a =10) [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Numerical Resultsmentioning

confidence: 99%

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A face‐based monolithic approach for the incompressible magnetohydrodynamics equations

Ata

Şahin

2019

Numerical Methods in Fluids

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Summary A novel numerical algorithm has been developed to solve the incompressible resistive magnetohydrodynamics equations in a fully coupled form. The numerical method is based on the face‐centered unstructured finite volume approximation, where the velocity and magnetic field vector components are defined at the center of edges/faces; meanwhile, the pressure term is defined at element centroid. In order to enforce a divergence‐free magnetic field, the gradient of a scalar Lagrange multiplier is introduced into the induction equation. A special attention will be given to satisfy the continuity equation and the Gauss' law for magnetism within each element and the summation of the equations can be exactly reduced to the domain boundary. The first modification to the original algorithm involves the evaluation of the convective fluxes over the two neighboring elements, where the discrete continuity equations are exactly satisfied. The second modification is based on the neglecting electric field term from the Lorentz force in two dimensions. The resulting large‐scale algebraic linear equations are solved in a fully coupled manner using the one‐ and two‐level restricted additive Schwarz preconditioners to avoid any time step restrictions forced by stability requirements. The spatial convergence of the algorithm is confirmed by solving the Hartmann flow, and then the algorithm is applied to the classical lid‐driven cavity and backward facing step benchmark problems in two and three dimensions. The lid‐driven cavity flow calculations at relatively high Stuart numbers indicate the perfect braking effect of the magnetic field in two dimensions.

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Section: Numerical Resultsmentioning

confidence: 75%

Section: Numerical Resultsmentioning

confidence: 99%

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A face‐based monolithic approach for the incompressible magnetohydrodynamics equations

Ata

Şahin

2019

Numerical Methods in Fluids

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“…Consequently a new class of effective constructions were proposed to overcome these shortcomings such as domain decomposition [23], the improved truncated singular valued decomposition [24], the localized formulations [25,26], fast multipole expansion techniques [27], etc. Among these new techniques, local scheme based on local support interpolations appears to more efficient in handling a large number of collocation points and less sensitive to changes of shape parameter [9,17,18,19,20,21,22,28,29].…”

Section: Introductionmentioning

confidence: 99%

Localized method of approximate particular solutions for solving unsteady Navier–Stokes problem

Zhang

Chen

et al. 2016

Applied Mathematical Modelling

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Highlights• The LMAPS is proposed to solve Navier-Stokes equations.• The weighting coefficients are obtained by local MQ-RBFs.• A global and sparse matrix is reformulated.• Fractional step algorithm is adopted. AbstractThe localized method of approximate particular solutions (LMAPS) is proposed to solve two-dimensional transient incompressible Navier-Stokes systems of equations in primitive variables. The equations contain the Laplacian operator. In avoiding ill-conditioning problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear system within local supporting domain in which five nearest neighboring points and multiquadrics are used for interpolation. Then local matrices are reformulated in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The method is assessed on driven cavity problem and flow around cylinder. The numerical experiments show that the newly developed LMAPS is suitable for solving incompressible Navier-Stokes equations with high accuracy and efficiency.

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“…Lee et al (2003) first proposed the local RBF collocation method (LRBFCM) based on the multiquadric RBF (Hardy, 1971). The LRBFCM has been applied to interdisciplinary fields, such as diffusion problems (Šarler and Vertnik, 2006), Darcy flow in porous media (Kosec and Sarler, 2008), magneto-hydrodynamic problems (Mramor et al, 2013), sociological problems (Dehghan et al, 2015), differential quadrature methods (Dehghan and Nikpour, 2013) and others. In addition, there are also researches using the particular solutions of multiquadrics to improve the accuracy (Tsai, 2013(Tsai, , 2015Yao et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Using a local radial basis function collocation method to approximate radiation boundary conditions

2015

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Simulation of laminar backward facing step flow under magnetic field with explicit local radial basis function collocation method

Cited by 35 publications

References 41 publications

A face‐based monolithic approach for the incompressible magnetohydrodynamics equations

A face‐based monolithic approach for the incompressible magnetohydrodynamics equations

Localized method of approximate particular solutions for solving unsteady Navier–Stokes problem

Using a local radial basis function collocation method to approximate radiation boundary conditions

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