Solving natural convection heat transfer in turbulent flow by extending the meshless local Petrov–Galerkin method

Sheikhi, Nasrin; Najafi, Mohammad; Enjilela, Vali

doi:10.1016/j.enganabound.2018.03.018

Cited by 17 publications

(6 citation statements)

References 37 publications

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“…This algorithm reduces the computational cost of boundary element method (BEM), significantly, when more accurate results are requested. In a more detailed review of the meshless literature for fluid flow problems, we find several types of research in both 2 D and 3 D …”

Section: Introductionmentioning

confidence: 99%

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

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Summary In this paper, we propose for the first time to extend the application field of the high‐order mesh‐free approach to the stationary incompressible Navier‐Stokes equations. This approach is based on a high‐order algorithm, which combines a Taylor series expansion, a continuation technique, and a moving least squares (MLS) method. The Taylor series expansion permits to transform the nonlinear problem into a succession of continuous linear ones with the same tangent operator. The MLS method is used to transform the succession of continuous linear problems into discrete ones. The continuation technique allows to compute step‐by‐step the whole solution of the discrete problems. This mesh‐free approach is tested on three examples: a flow around a cylindrical obstacle, a flow in a sudden expansion, and the standard benchmark lid‐driven cavity flow. A comparison of the obtained results with those computed by the Newton‐Raphson method with MLS, the high‐order continuation with finite element method, and those of literature is presented.

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Section: Introductionmentioning

confidence: 99%

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

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“…The MLPG method has been employed in a variety of continuum problems. Its application include steady state (Wu and Tao, 2008) and transient heat conduction (Batra et al, 2004;Thakur et al, 2010), natural convection (Aredfmanesh et al, 2010;Sheikhi et al, 2018), radiative heat transfer (Liu, 2006;Tian and Rao, 2012), phase change problems (Morimoto et al, 2016;Thakur et al, 2011), elastostatics (Atluri and Zhu, 2000;Sladek et al, 2004), elastodynamics (Gu and Liu, 2001;Sladek et al, 2003;Soares et al, 2009), crack propagation (Gao et al, 2006;Sladek et al, 2007) and multi-physics problems Sladek et al (2008). The MLPG method has also been used in collaboration, with finite volume (Atluri et al, 2004) and collocation method, to solve inverse heat transfer problems (Zhang et al, 2014) and transient diffusion problems (Mountris and Pueyo, 2020), respectively.…”

Section: Gmres Solvermentioning

confidence: 99%

The GMRES solver for the interpolating meshless local Petrov–Galerkin method applied to heat conduction

Singh

2021

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PurposeThe work presents a novel implementation of the generalized minimum residual (GMRES) solver in conjunction with the interpolating meshless local Petrov–Galerkin (MLPG) method to solve steady-state heat conduction in 2-D as well as in 3-D domains.Design/methodology/approachThe restarted version of the GMRES solver (with and without preconditioner) is applied to solve an asymmetric system of equations, arising due to the interpolating MLPG formulation. Its performance is compared with the biconjugate gradient stabilized (BiCGSTAB) solver on the basis of computation time and convergence behaviour. Jacobi and successive over-relaxation (SOR) methods are used as the preconditioners in both the solvers.FindingsThe results show that the GMRES solver outperforms the BiCGSTAB solver in terms of smoothness of convergence behaviour, while performs slightly better than the BiCGSTAB method in terms of Central processing Unit (CPU) time.Originality/valueMLPG formulation leads to a non-symmetric system of algebraic equations. Iterative methods such as GMRES and BiCGSTAB methods are required for its solution for large-scale problems. This work presents the use of GMRES solver with the MLPG method for the very first time.

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“…Application of MLPG includes steady state (Wu and Tao, 2008) and non linear heat conduction (Batra et al, 2004;Thakur, 2021), natural convection (Aredfmanesh et al, 2010;Sheikhi et al, 2018), radiative heat transfer (Liu, 2006;Tian and Rao, 2012), phase change problems (Morimoto et al, 2016;Thakur et al, 2011), elastostatics (Atluri and Zhu, 2000;Sladek et al, 2004), elastodynamics (Gu and Liu, 2001;Sladek et al, 2003;Soares et al, 2009), crack propagation (Gao et al, 2006;Sladek et al, 2007), ocean engineering (Sriram and Ma, 2021), hydrology (Abdi et al, 2022;Mohtashami et al, 2022), solidification (Bouzgarrou et al, 2021) and multi-physics problems (Sladek et al, 2008). For a comprehensive review of MLPG applications, please refer to Atluri (2002), Sladek et al (2013), andSingh (2018).…”

Section: Introductionmentioning

confidence: 99%

“…, 2004; Thakur, 2021), natural convection (Aredfmanesh et al. , 2010; Sheikhi et al. , 2018), radiative heat transfer (Liu, 2006; Tian and Rao, 2012), phase change problems (Morimoto et al.…”

Section: Introductionmentioning

confidence: 99%

OpenMP-based parallel MLPG solver for analysis of heat conduction

Singh,

Singh

2024

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PurposeIn the present work, we focus on developing an in-house parallel meshless local Petrov-Galerkin (MLPG) code for the analysis of heat conduction in two-dimensional and three-dimensional regular as well as complex geometries.Design/methodology/approachThe parallel MLPG code has been implemented using open multi-processing (OpenMP) application programming interface (API) on the shared memory multicore CPU architecture. Numerical simulations have been performed to find the critical regions of the serial code, and an OpenMP-based parallel MLPG code is developed, considering the critical regions of the sequential code.FindingsBased on performance parameters such as speed-up and parallel efficiency, the credibility of the parallelization procedure has been established. Maximum speed-up and parallel efficiency are 10.94 and 0.92 for regular three-dimensional geometry (343,000 nodes). Results demonstrate the suitability of parallelization for larger nodes as parallel efficiency and speed-up are more for the larger nodes.Originality/valueFew attempts have been made in parallel implementation of the MLPG method for solving large-scale industrial problems. Although the literature suggests that message-passing interface (MPI) based parallel MLPG codes have been developed, the OpenMP model has rarely been touched. This work is an attempt at the development of OpenMP-based parallel MLPG code for the very first time.

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Solving natural convection heat transfer in turbulent flow by extending the meshless local Petrov–Galerkin method

Cited by 17 publications

References 37 publications

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Solving the incompressible fluid flows by a high‐order mesh‐free approach

The GMRES solver for the interpolating meshless local Petrov–Galerkin method applied to heat conduction

OpenMP-based parallel MLPG solver for analysis of heat conduction

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