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Extending the meshless local Petrov-Galerkin method to solve stabilized turbulent fluid flow problems. (English) Zbl 1404.76165

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76F65 Direct numerical and large eddy simulation of turbulence
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[1] Arefmanesh, A.; Mahmoodi, M.; Nikfar, M., Effect of position of a square- shaped heat source on the Buoyancy-driven heat transfer in a square cavity filled with nanofluid, Sci. Iran., 21, 1129-1142, (2014)
[2] Arefmanesh, A.; Najafi, M.; Musavi, S. H., Buoyancy-driven fluid flow and heat transfer in a square cavity with a wavy baffle-Meshless numerical analysis, Eng. Anal. Bound. Elem., 37, 366-382, (2013) · Zbl 1351.76208
[3] Arefmanesh, A.; Najafi, M.; Nikfar, M., Meshless local Petrov-Galerkin simulation of Buoyancy-Driven fluid flow and heat transfer in a cavity with wavy side walls, Comput. Model. Eng. Sci., 62, 113-149, (2010) · Zbl 1231.76133
[4] Arefmanesh, A.; Najafi, M.; Nikfar, M., MLPG application of nanofluid flow mixed convection heat transfer in a wavy wall cavity, Comput. Model. Eng. Sci., 69, 91-117, (2010) · Zbl 1231.76302
[5] Arefmanesh, A.; Nikfar, M., Analysis of natural convection in a nanofluid-filled triangular enclosure induced by cold and hot sources on the walls using stabilized MLPG method, Can. J. chem. Eng., 91, 1711-1728, (2013)
[6] Atluri, S. N.; Zhu, T., A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Comput. Mech., 22, 117-127, (1998) · Zbl 0932.76067
[7] Barik, N. B.; Sekhar, T. V. S., An efficient local RBF meshless scheme for steady convection-diffusion problems, Int. J. Comput. Meth., 14, 1750064, (2017) · Zbl 1404.65288
[8] Cai, Y.; Han, L.; Tian, L.; Zhang, L., Meshless method based on Shepard function and partition of unity for two-dimensional crack problems, Eng. Anal. Bound. Elem., 65, 126-135, (2016) · Zbl 1403.74082
[9] Dehghan, M.; Abbaszadeh, M.; Mohebbi, A., Analysis of a meshless method for the time fractional diffusion-wave equation, Numer. Algorithm, 73, 445-476, (2016) · Zbl 1352.65298
[10] Dehghan, M.; Haghjoo-Saniji, M., The local radial point interpolation meshless method for solving Maxwell equations, Eng. Comput., 33, 897-918, (2017)
[11] Dehghan, M.; Mohammadi, V., A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method, Comput. Phys. Commun., 217, 23-34, (2017)
[12] Enjilela, V.; Arefmanesh, A., Two-step Taylor-characteristic-based MLPG method for fluid flow and heat transfer applications, Eng. Anal. Bound. Elem., 51, 174-190, (2015) · Zbl 1403.76043
[13] Enjilela, V.; Salimi, D.; Tavasoli, A.; Lotfi, M., Stabilized MLPG-VF-based method with CBS scheme for laminar flow at high Reynolds and Rayleigh numbers, Int. J. Mod. Phys. C, 27, 1650081, (2016)
[14] Hidayat, M. I. P.; Ariwahjoedi, B.; Parman, S.; Irawan, S., A mesh free approach for transient heat conduction analysis of nonlinear functionally graded materials, Int. J. Comput. Meth., 15, 1850007, (2018) · Zbl 1404.74202
[15] Hoffmann, K. L.; Chiang, S. T., Computational Fluid Dynamics, (2000), Engineering Education System: Engineering Education System, USA
[16] Hosseini, V. R.; Shivanian, E.; Chen, W., Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping, J. Comput. Phys., 307, 307-332, (2016) · Zbl 1352.65348
[17] Islam, S.; Singh, V., A local meshless method for steady state convection dominated flows, Int. J. Comput. Meth., 14, 1750067, (2017) · Zbl 1404.76195
[18] Jafari, N.; Azhari, M., Buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp-cloud method, Appl. Math. Comput., 313, 196-208, (2017)
[19] Ji, Y.; Huang, T.; Huang, W.; Rong, L., Meshfree method in geophysical electromagnetic prospecting: The 2D magnetotelluric example, Int. J. Comput. Meth., 14, 1750084, (2017) · Zbl 1404.86033
[20] Jovic, S. and Driver, D. M. [1994] “Backward-facing step measurements at low Reynolds number, \(\text{Re}_H = 5 0 0 0\),” NASA technical memorandum 108807, pp. 21-24, https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19940028784.pdf.
[21] Latin, R. M.; Bowersox, R. D. W., Flow properties of a supersonic turbulent boundary layer with wall roughness, AIAA J., 38, 1804-1821, (2000)
[22] Laufer, J. [1951] “Investigation of turbulent flow in a two-dimensional channel,” NACA Report1053.
[23] Le, H.; Moin, P.; Kim, J., Dirct numerical simulation of turbulent flow over a backward-facing step, J. Fluid Mech., 330, 349-374, (1997) · Zbl 0900.76367
[24] Lei, Z. X.; Zhang, L. W.; Liew, K. M., Meshless modeling of geometrically nonlinear behavior of CNT-reinforced functionally graded composite laminated plates, Appl. Math. Comput., 295, 24-46, (2017)
[25] Lin, H.; Atluri, S. N., The meshless local Petrov-Galerkin (MLPG) method for solving incompressible Navier-Stokes equations, Comput. Model. Eng. Sci., 2, 117-142, (2001)
[26] Liu, Ch. Sh.; Younga, D. L., A multiple-scale Pascal polynomial for 2D Stokes and inverse Cauchy-Stokes problems, J. Comput. Phys., 312, 1-13, (2016) · Zbl 1351.76219
[27] Loukopoulos, V. C.; Bourantas, G. C., MLPG6 for the solution of incompressible flow equations, Comput. Model. Eng. Sci., 88, 531-558, (2012) · Zbl 1356.76059
[28] Mardani, A.; Hooshmandasl, M. R.; Hosseini, M. M.; Heydari, M. H., Moving least squares (MLS) method for the nonlinear hyperbolic telegraph equation with variable coefficients, Int. J. Comput. Meth., 14, 1750026, (2017) · Zbl 1404.65199
[29] Mohammadi, M. H., Stabilized meshless local Petrov-Galerkin (MLPG) method for incompressible viscous fluid flows, Comput. Model. Eng. Sci., 29, 75-94, (2008) · Zbl 1232.76028
[30] Najafi, M.; Arefmanesh, A.; Enjilela, V., Meshless local Petrov-Galerkin method-higher Reynolds numbers fluid flow applications, Eng. Anal. Bound. Elem., 36, 1671-1685, (2012) · Zbl 1351.76073
[31] Najafi, M.; Arefmanesh, A.; Enjilela, V., Extending MLPG primitive variable-based method for implementation in fluid flow and natural, forced and mixed convection heat transfer, Eng. Anal. Bound. Elem., 37, 1285-1299, (2013) · Zbl 1287.65081
[32] Najafi, M.; Enjilela, V., Natural convection heat transfer at high Rayleigh numbers — Extended meshless local Petrov-Galerkin (MLPG) primitive variable method, Eng. Anal. Bound. Elem., 44, 170-184, (2014) · Zbl 1297.80003
[33] Najafi, M.; Nikfar, M.; Arefmanesh, A., Inclination angle implications for fluid flow convection in complex geometry enclosure numerical analyses, J. Theor. Appl. Mech., 53, 519-530, (2015)
[34] Nikfar, M.; Mahmoodi, M., Meshless local Petrov-Galerkin analysis of free convection on nanofluid in a cavity with wavy side walls, Eng. Anal. Bound. Elem., 36, 433-445, (2012) · Zbl 1245.76141
[35] Nithiarasu, P.; Liu, C. B., An artificial compressibility based characteristic based split (CBS) scheme for steady and unsteady turbulent incompressible flows, Comput. Meth. Appl. Mech. Eng., 195, 2961-2982, (2006) · Zbl 1176.76086
[36] Pope, S. B., Turbulent Flows, (2000), Cambridge University Press: Cambridge University Press, New York · Zbl 0966.76002
[37] Rumsey, C. [2012]. NASA Langley turbulence modeling resource, http://turbmodels.larc.nasa.gov.
[38] Sharif, M. A. R.; Guo, G., Computational analysis of supersonic turbulent boundary layers over rough surfaces using the k-x and the stress-x models, Appl. Math. Model., 31, 2655-2667, (2007) · Zbl 1225.76180
[39] Skouras, E. D.; Bourantas, G. C.; Loukopoulos, V. C.; Nikiforidis, G. C., Truly meshless localized type techniques for the steady-state heat conduction problems for isotropic and functionally graded materials, Eng. Anal. Bound. Elem., 35, 452-464, (2011) · Zbl 1259.80029
[40] Stevens, D.; Power, H., The radial basis function finite collocation approach for capturing sharp fronts in time dependent advection problems, J. Comput. Phys., 298, 423-445, (2015) · Zbl 1349.65526
[41] Vertnik, R.; Šarler, B., Solution of incompressible turbulent flow by a mesh-free method, Comput. Model. Eng. Sci., 44, 65-95, (2009) · Zbl 1357.76030
[42] Wu, X. H.; Tao, W. Q.; Shen, Sh. P.; Zhu, X. W., A stabilized MLPG method for steady state incompressible fluid flow simulation, J. Comput. Phys., 229, 8564-8577, (2010) · Zbl 1381.76272
[43] Wu, Y. L.; Liu, G. R.; Gu, Y. T., Application of meshless local Petrov-Galerkin (MLPG) approach to simulation of incompressible flow, Numer. Heat Transf. B, 48, 459-475, (2005)
[44] Xiao, L.; Yang, J.; Peng, T.; Tao, L., A free surface interpolation approach for rapid simulation of short waves in meshless numerical wave tank based on the radial basis function, J. Comput. Phys., 307, 203-224, (2016) · Zbl 1351.76228
[45] Yang, J.; Hu, H.; Koutsawa, Y.; Ferry, M. P., Taylor meshless method for solving non-linear partial differential equations, J. Comput. Phys., 348, 385-400, (2017) · Zbl 1380.65393
[46] Zheng, H.; Zhang, Ch.; Wang, Y.; Sladek, J.; Sladek, V., A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals, J. Comput. Phys., 305, 997-1014, (2016) · Zbl 1349.74380
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