Keywords and phrases: natural convection, enclose cavities, localized RBF, meshless method.
Received: March 24, 2022; Revised: April 26, 2022; Accepted: May 13, 2022; Published: July 15, 2022
How to cite this article: Mohamed Jeyar, Elmiloud Chaabelsri, Marwane Bensaad and Driss Achemlal, A meshless numerical method based on RBF with artificial compressibility to simulate natural heat convection in enclosed cavities, JP Journal of Heat and Mass Transfer 28 (2022), 15-34. http://dx.doi.org/10.17654/0973576322031
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] D. Das, M. Roy and T. Basak, Studies on natural convection within enclosures of various (non-square) shapes - a review, Int. J. Heat Mass Transf. 106 (2017), 356-406. doi: 10.1016/j.ijheatmasstransfer.2016.08.034. [2] A. Dalal and M. K. Das, Natural convection in a cavity with a wavy wall heated from below and uniformly cooled from the top and both sides, J. Heat Transfer 128(7) (2006), 717-725. doi: 10.1115/1.2194044. [3] M. Ashjaee, M. Amiri and J. Rostami, A correlation for free convection heat transfer from vertical wavy surfaces, Heat Mass Transf. 44(1) (2007), 101-111. doi: 10.1007/s00231-006-0221-8. [4] Y. Varol and H. F. Oztop, Buoyancy induced heat transfer and fluid flow inside a tilted wavy solar collector, Build. Environ. 42(5) (2007), 2062-2071. doi: 10.1016/j.buildenv.2006.03.001. [5] M. K. Triveni and R. Panua, Numerical simulation of natural convection in a triangular enclosure with caterpillar (C)-curve shape hot wall, Int. J. Heat Mass Transf. 96 (2016), 535-547. doi: 10.1016/j.ijheatmasstransfer.2016.02.002. [6] Y. L. Wu, A meshless local radial point interpolation method (LRPIM) for fluid flow problems, Advances in Meshfree and X-FEM Methods (2002), 129-134. doi: 10.1142/9789812778611_0021. [7] K. Szewc, J. Pozorski and A. Tanière, Modeling of natural convection with smoothed particle hydrodynamics: non-Boussinesq formulation, Int. J. Heat Mass Transf. 54(23-24) (2011), 4807-4816. doi: 10.1016/j.ijheatmasstransfer.2011.06.034. [8] X. Zhang and P. Zhang, Meshless modeling of natural convection problems in non-rectangular cavity using the variational multiscale element free Galerkin method, Eng. Anal. Bound. Elem. 61 (2015), 287-300. doi: 10.1016/j.enganabound.2015.08.005. [9] E. H. Ooi and V. Popov, Meshless solution of two-dimensional incompressible flow problems using the radial basis integral equation method, Appl. Math. Model. 37(20-21) (2013), 8985-8998. doi: 10.1016/j.apm.2013.04.035. [10] E. J. Kansa, Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates, Comput. Math. Appl. 19(8-9) (1990), 127-145. doi: 10.1016/0898-1221(90)90270-T. [11] E. Divo and A. J. Kassab, Localized meshless modeling of natural-convective viscous flows, Numer. Heat Transf. Part B Fundam. 53(6) (2008), 487-509. doi: 10.1080/10407790802083190. [12] G. Kosec and B. Šarler, Solution of thermo-fluid problems by collocation with local pressure correction, Int. J. Numer. Methods Heat Fluid Flow 18(7/8) (2008), 868-882. doi: 10.1108/09615530810898999. [13] Soheil Soleimani, Nima Sedaghatizadeh, D. D. Ganji, A. Asgharian and Iman Marzaban Shirkharkolay, Numerical simulation of two dimensional stokes flow between eccentric rotating circular cylinders, AIP Conference Proceedings 1400 (2011), 574-578. https://doi.org/10.1063/1.3663184. [14] E. J. Kansa, Exact explicit time integration of hyperbolic partial differential equations with mesh free radial basis functions, Eng. Anal. Bound. Elem. 31(7) (2007), 577-585. doi: 10.1016/j.enganabound.2006.12.001. [15] Pranowo and A. T. Wijayanta, Numerical solution strategy for natural convection problems in a triangular cavity using a direct meshless local Petrov-Galerkin method combined with an implicit artificial-compressibility model, Eng. Anal. Bound. Elem. 126 (2021), 13-29. doi: 10.1016/j.enganabound.2021.02.006. [16] A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2(1) (1967), 12-26. doi: 10.1016/0021-9991(67)90037-X. [17] E. Chaabelasri, Numerical simulation of dam break flows using a radial basis function meshless method with artificial viscosity, Model. Simul. Eng. 2018 (2018), 1-11. doi: 10.1155/2018/4245658. [18] E. Chaabelasri, M. Jeyar and A. G. L. Borthwick, Explicit radial basis function collocation method for computing shallow water flows, Procedia Comput. Sci. 148 (2019), 361-370. doi: 10.1016/j.procs.2019.01.044. [19] S. A. Sarra, A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains, Appl. Math. Comput. 218(19) (2012), 9853-9865. doi: 10.1016/j.amc.2012.03.062. [20] G. De Vahl Davis, Natural convection of air in a square cavity a bench mark numerical solution, Numerical Methods in Fluids 3 (1983), 249-264. [21] S. Völker, T. Burton and S. P. Vanka, Finite-volume multigrid calculation of natural-convection flows on unstructured grids, Numer. Heat Transf. Part B Fundam. 30(1) (1996), 1-22. doi: 10.1080/10407799608915069.
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