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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 48, 2005 - Issue 5
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Original Articles

Application of Meshless Local Petrov-Galerkin (MLPG) Approach to Simulation of Incompressible Flow

Y. L. Wu Centre for ACES, Department of Mechanical Engineering, National University of Singapore, Singapore
,
G. R. Liu Centre for ACES, Department of Mechanical Engineering, National University of Singapore, SingaporeCorrespondence[email protected]
&
Y. T. Gu Centre for ACES, Department of Mechanical Engineering, National University of Singapore, Singapore
Pages 459-475 | Received 28 Mar 2005, Accepted 20 May 2005, Published online: 01 Sep 2006

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Peyman Mayeli & Gregory J. Sheard. (2021) A simplified and efficient Gay-Lussac approach for non-Boussinesq treatment of natural convection problems. Numerical Heat Transfer, Part B: Fundamentals 80:5-6, pages 115-135.
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Ali Ashrafizadeh & Mehdi Nikfar. (2016) On the numerical solution of generalized convection heat transfer problems via the method of proper closure equations – part II: Application to test problems. Numerical Heat Transfer, Part A: Applications 70:2, pages 204-222.
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Elshan Soltani & Mehdi Badri Ghomizad. (2016) Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation. Numerical Heat Transfer, Part B: Fundamentals 70:1, pages 25-46.
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Tien-Mo Shih, Martinus Arie & Derrick Ko. (2011) Literature Survey of Numerical Heat Transfer (2000–2009): Part II. Numerical Heat Transfer, Part A: Applications 60:11-12, pages 883-1096.
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Chia-Ming Fan & Hsin-Fang Chan. (2011) Modified Collocation Trefftz Method for the Geometry Boundary Identification Problem of Heat Conduction. Numerical Heat Transfer, Part B: Fundamentals 59:1, pages 58-75.
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Ming Li, C. S. Chen & C. H. Tsai. (2010) Meshless Method Based on Radial Basis Functions for Solving Parabolic Partial Differential Equations with Variable Coefficients. Numerical Heat Transfer, Part B: Fundamentals 57:5, pages 333-347.
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Eduardo Divo & AlainJ. Kassab. (2008) Localized Meshless Modeling of Natural-Convective Viscous Flows. Numerical Heat Transfer, Part B: Fundamentals 53:6, pages 487-509.
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Rusty Rook, Mehmet Yildiz & Sadik Dost. (2007) Modeling Transient Heat Transfer Using SPH and Implicit Time Integration. Numerical Heat Transfer, Part B: Fundamentals 51:1, pages 1-23.
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Shima Nesari Haghighi Fard, Mohammad Najafi, Vali Enjilela, Ali Imam & Arash Karimipour. (2023) Application extension of the meshless local Petrov-Galerkin method: Non-Newtonian fluid flow implementations. Engineering Analysis with Boundary Elements 156, pages 321-343.
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K. Swetha, T. I. Eldho, L. Guneshwor Singh & A. Vinod Kumar. (2022) Simulation of coupled flow and contaminant transport in an unconfined aquifer using the local radial point interpolation meshless methodSimulation d’un écoulement couplé à un transport de contaminant dans un aquifère libre, utilisant la méthode d’interpolation du point radial local sans maillageSimulación del flujo acoplado y del transporte de contaminantes en un acuífero no confinado utilizando el método sin malla de interpolación radial local使用局部径向点插值无网格方法耦合模拟非承压含水层中的水流和污染物运移Simulação de fluxo acoplado e transporte de contaminante em aquífero não confinado utilizando o método de interpolação de ponto radial local sem malha. Hydrogeology Journal 31:2, pages 485-500.
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George C. Bourantas, Benjamin F. Zwick, Theo Philippe Lavier, Vassilios C. Loukopoulos, Athanassios A. Dimas, Adam Wittek & Karol Miller. (2022) An immersed boundary vector potential‐vorticity meshless solver of the incompressible Navier–Stokes equation. International Journal for Numerical Methods in Fluids 95:1, pages 143-175.
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Flávio dos Ramos de Sousa Mendonça, Wilber Humberto Vélez Gómez & Artur António de Almeida Portela. (2022) A local meshless numeric method applied in free and forced vibration analyses for elastic problems. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44:8.
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Peyman Mayeli & Gregory J. Sheard. (2021) An efficient and simplified Gay‐Lussac approach in secondary variables form for the non‐Boussinesq simulation of free convection problems . International Journal for Numerical Methods in Fluids 93:11, pages 3264-3279.
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Peyman Mayeli & Gregory J. Sheard. (2021) Natural convection and entropy generation in square and skew cavities due to large temperature differences: A  Gay–Lussac ‐type vorticity stream‐function approach . International Journal for Numerical Methods in Fluids 93:7, pages 2396-2420.
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Vali Enjilela, Elshan Soltani, Mohsen Ghadyani & Rasul Bagheri. (2020) Numerical investigation of the effect of temperature variation on heat transfer rate in a square cavity filled water-Al2O3 nanofluid with a hot circular cylinder in the center of the cavity. International Journal of Modern Physics C 32:03, pages 2150030.
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Peyman Mayeli & Gregory J. Sheard. (2020) A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem. International Journal for Numerical Methods in Fluids 93:3, pages 683-702.
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J.M. Granados, C.A. Bustamante & W.F. Florez. (2021) Extending meshless method of approximate particular solutions (MAPS) to two-dimensional convection heat transfer problems.. Applied Mathematics and Computation 390, pages 125484.
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Nasrin Sheikhi, Mohammad Najafi & Vali Enjilela. (2019) Modifying a meshless method to solving κ−ε turbulent natural convection heat transfer. International Journal of Modern Physics C 31:01, pages 2050014.
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Bourantas, Zwick, Joldes, Loukopoulos, Tavner, Wittek & Miller. (2019) An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations. Fluids 4:3, pages 164.
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Nasrin Sheikhi, Mohammad Najafi & Vali Enjilela. (2018) Extending the Meshless Local Petrov–Galerkin Method to Solve Stabilized Turbulent Fluid Flow Problems. International Journal of Computational Methods 16:01, pages 1850086.
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Nasrin Sheikhi, Mohammad Najafi & Vali Enjilela. (2018) Solving natural convection heat transfer in turbulent flow by extending the meshless local Petrov–Galerkin method. Engineering Analysis with Boundary Elements 93, pages 29-43.
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Mehdi Dehghan & Mostafa Abbaszadeh. (2018) Solution of multi-dimensional Klein–Gordon–Zakharov and Schrödinger/Gross–Pitaevskii equations via local Radial Basis Functions–Differential Quadrature (RBF–DQ) technique on non-rectangular computational domains. Engineering Analysis with Boundary Elements 92, pages 156-170.
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George C. Bourantas, Bevan L. Cheeseman, Rajesh Ramaswamy & Ivo F. Sbalzarini. (2016) Using DC PSE operator discretization in Eulerian meshless collocation methods improves their robustness in complex geometries. Computers & Fluids 136, pages 285-300.
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Vali Enjilela, Davood Salimi, Ali Tavasoli & Mohsen Lotfi. (2016) Stabilized MLPG-VF-based method with CBS scheme for laminar flow at high Reynolds and Rayleigh numbers. International Journal of Modern Physics C 27:07, pages 1650081.
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Kamiar Zamzamian & M.Y. Hashemi. (2015) A novel meshless method for incompressible flow calculations. Engineering Analysis with Boundary Elements 56, pages 106-118.
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C. Sataprahm & A. Luadsong. (2014) The meshless local Petrov-Galerkin method for simulating unsteady incompressible fluid flow. Journal of the Egyptian Mathematical Society 22:3, pages 501-510.
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H.C.P. Karunasena, W. Senadeera, Y.T. Gu & R.J. Brown. (2014) A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying. Applied Mathematical Modelling 38:15-16, pages 3781-3801.
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H.C.P. Karunasena, W. Senadeera, R.J. Brown & Y.T. Gu. (2014) Simulation of plant cell shrinkage during drying – A SPH–DEM approach. Engineering Analysis with Boundary Elements 44, pages 1-18.
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Mohammad Najafi & Vali Enjilela. (2014) Natural convection heat transfer at high Rayleigh numbers – Extended meshless local Petrov–Galerkin (MLPG) primitive variable method. Engineering Analysis with Boundary Elements 44, pages 170-184.
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Mohammad Najafi, Ali Arefmanesh & Vali Enjilela. (2013) Extending MLPG primitive variable-based method for implementation in fluid flow and natural, forced and mixed convection heat transfer. Engineering Analysis with Boundary Elements 37:10, pages 1285-1299.
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S. Wang, B.C. Khoo, G.R. Liu & G.X. Xu. (2013) An arbitrary Lagrangian–Eulerian gradient smoothing method (GSM/ALE) for interaction of fluid and a moving rigid body. Computers & Fluids 71, pages 327-347.
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Mehdi Nikfar & Mostafa Mahmoodi. (2012) Meshless local Petrov–Galerkin analysis of free convection of nanofluid in a cavity with wavy side walls. Engineering Analysis with Boundary Elements 36:3, pages 433-445.
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R. Trobec, G. Kosec, M. Šterk & B. Šarler. (2012) Comparison of local weak and strong form meshless methods for 2-D diffusion equation. Engineering Analysis with Boundary Elements 36:3, pages 310-321.
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M. J. Mahmoodabadi, R. Abedzadeh Maafi, A. Bagheri & G. H. Baradaran. (2015) Meshless Local Petrov-Galerkin Method for 3D Steady-State Heat Conduction Problems. Advances in Mechanical Engineering 3, pages 251546.
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Xue-Hong Wu, Wen-Quan Tao, Sheng-Ping Shen & Xing-Wang Zhu. (2010) A stabilized MLPG method for steady state incompressible fluid flow simulation. Journal of Computational Physics 229:22, pages 8564-8577.
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Soheil Soleimani, M. Jalaal, H. Bararnia, E. Ghasemi, D.D. Ganji & F. Mohammadi. (2010) Local RBF-DQ method for two-dimensional transient heat conduction problems. International Communications in Heat and Mass Transfer 37:9, pages 1411-1418.
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K Le-Cao, N Mai-Duy, C-D Tran & T Tran-Cong. (2010) A new integrated-rbf-based domain-embedding scheme for solving fluid-flow problems. IOP Conference Series: Materials Science and Engineering 10, pages 012021.
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S.P. Hu, C.M. Fan & D.L. Young. (2010) The meshless analog equation method for solving heat transfer to molten polymer flow in tubes. International Journal of Heat and Mass Transfer 53:9-10, pages 2240-2247.
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Xue-Hong Wu & Wen-Quan Tao. (2008) Meshless method based on the local weak-forms for steady-state heat conduction problems. International Journal of Heat and Mass Transfer 51:11-12, pages 3103-3112.
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ABAZAR SHAMEKHI & KAYVAN SADEGHY. (2011) LID-DRIVEN CAVITY SIMULATION BY MESH-FREE METHOD. International Journal of Computational Methods 04:03, pages 397-415.
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Zhi-bo Tang & Qiang Li. (2007) Advances in research of stress-assisted corrosion fatigue problem. Journal of Zhejiang University-SCIENCE A 8:2, pages 221-227.
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Rusty Rook & Sadik Dost. (2007) The use of smoothed particle hydrodynamics for simulating crystal growth from solution. International Journal of Engineering Science 45:1, pages 75-93.
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