A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows. (English) Zbl 07875925
Keywords:
Hermite-type; collocation; mesh-free method; weighted least squares; dimensionless shape-function; incompressible fluid flowReferences:
| [1] | Alleborn, N.; Nandakumar, K.; Raszillier, H.; Durst, F., Further contributions on the two-dimensional flow in a sudden expansion, J. Fluid Mech., 330, 169-188, 1997 · Zbl 0894.76023 |
| [2] | Allery, C.; Cadou, J. M.; Hamdouni, A.; Razafindralandy, D., Application of the asymptotic numerical method to the coanda effect study, Revue Eur. Éléments Finis, 13, 1-2, 57-77, 2004 · Zbl 1147.76600 |
| [3] | Armaly, B. F.; Durst, F.; Pereira, J.; Schönung, B., Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 127, 473-496, 1983 |
| [4] | Askour, O.; Mesmoudi, S.; Tri, A.; Braikat, B.; Zahrouni, H.; Potier-Ferry, M., Method of fundamental solutions and a high order continuation for bifurcation analysis within Föppl-von Karman plate theory, Eng. Anal. Bound. Elem., 120, 67-72, 2020 · Zbl 1464.74384 |
| [5] | Battaglia, F.; Tavener, S. J.; Kulkarni, A. K.; Merkle, C. L., Bifurcation of low Reynolds number flows in symmetric channels, AIAA J., 35, 1, 99-105, 1997 · Zbl 0893.76012 |
| [6] | Ben-Artzi, M.; Croisille, J. P.; Fishelov, D.; Trachtenberg, S., A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations, J. Comput. Phys., 205, 2, 640-664, 2005 · Zbl 1087.76025 |
| [7] | Cadou, J. M.; Potier-Ferry, M.; Cochelin, B.; Damil, N., ANM for stationary Navier-Ntokes equations and with Petrov-Galerkin formulation, Internat. J. Numer. Methods Engrg., 50, 4, 825-845, 2001 · Zbl 1013.76046 |
| [8] | Chandrakant, S.; Panchal, H.; Sadasivuni, K. K., Numerical simulation of flow-through heat exchanger having helical flow passage using high order accurate solution dependent weighted least square based gradient calculations, Energy Sourc., Part A: Recovery, Util. Environ. Effects, 1-26, 2021 |
| [9] | Chen, J.; Yu, P.; Tian, Z. F.; Ouyang, H., A high-order compact scheme for solving the 2D steady incompressible Navier-Stokes equations in general curvilinear coordinates, Internat. J. Numer. Methods Fluids, 92, 5, 456-477, 2020 |
| [10] | Cherdron, W.; Durst, F.; Whitelaw, J. H., Asymmetric flows and instabilities in symmetric ducts with sudden expansions, J. Fluid Mech., 84, 1, 13-31, 1978 |
| [11] | Chinchapatnam, P. P.; Djidjeli, K.; Nair, P. B., Radial basis function meshless method for the steady incompressible Navier-Stokes equations, Int. J. Comput. Math., 84, 10, 1509-1521, 2007 · Zbl 1123.76048 |
| [12] | Chow, C. Y.; Huang, M. K.; Yan, C. Z., Unsteady flow about a Joukowski airfoil in the presence of moving vortices, AIAA J., 23, 5, 657-658, 1985 |
| [13] | Cochelin, B.; Medale, M., Power series analysis as a major breakthrough to improve the efficiency of asymptotic numerical method in the vicinity of bifurcations, J. Comput. Phys., 236, 594-607, 2013 |
| [14] | Drikakis, D., Bifurcation phenomena in incompressible sudden expansion flows, Phys. Fluids, 9, 1, 76-87, 1997 |
| [15] | Elmhaia, O.; Belaasilia, Y.; Askour, O.; Braikat, B.; Damil, N., An efficient mesh-free approach for the determination of stresses intensity factors, Eng. Anal. Bound. Elem., 133, 49-60, 2021 · Zbl 1521.74409 |
| [16] | Elmhaia, O.; Belaasilia, Y.; Askour, O.; Braikat, B.; Damil, N., Numerical analysis of frictional contact between crack lips in the framework of linear elastic fracture mechanics by a mesh-free approach, Theor. Appl. Fract. Mech., Article 103749 pp., 2023 |
| [17] | Elmhaia, O.; Belaasilia, Y.; Braikat, B.; Damil, N., Solving non-linear elasticity problems by a WLS high order continuation, (International Conference on Computational Science, 2020, Springer), 266-279 |
| [18] | Fearn, R. M.; Mullin, T.; Cliffe, K. A., Nonlinear flow phenomena in a symmetric sudden expansion, J. Fluid Mech., 211, 595-608, 1990 |
| [19] | Felter, C. L.; Walther, J. H.; Henriksen, C., Moving least squares simulation of free surface flows, Comput. & Fluids, 91, 47-56, 2014 · Zbl 1391.76471 |
| [20] | Fortin, A.; Jardak, M.; Gervais, J. J.; Pierre, R., Localization of Hopf bifurcations in fluid flow problems, Internat. J. Numer. Methods Fluids, 24, 11, 1185-1210, 1997 · Zbl 0886.76042 |
| [21] | Ghia, U.; Ghia, K. N.; Shin, C. T., High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48, 3, 387-411, 1982 · Zbl 0511.76031 |
| [22] | Ghia, K. N.; Osswald, G. A.; Ghia, U., Analysis of incompressible massively separated viscous flows using unsteady Navier-Stokes equations, Internat. J. Numer. Methods Fluids, 9, 8, 1025-1050, 1989 · Zbl 0683.76027 |
| [23] | Gresho, P. M.; Gartling, D. K.; Torczynski, J. R.; Cliffe, K. A.; Winters, K. H.; Garratt, T. J.; Spence, A.; Goodrich, J. W., Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re=800 stable?, Internat. J. Numer. Methods Fluids, 17, 6, 501-541, 1993 · Zbl 0784.76050 |
| [24] | Guevel, Y.; Girault, G.; Cadou, J. M., Parametric analysis of steady bifurcations in 2D incompressible viscous flow with high order algorithm, Comput. & Fluids, 100, 185-195, 2014 · Zbl 1391.76546 |
| [25] | Hilali, Y.; Bourihane, O., A mixed MLS and Hermite-type MLS method for buckling and postbuckling analysis of thin plates, Structures, 33, 2349-2360, 2021 |
| [26] | Huerta, A.; Vidal, Y.; Villon, P., Pseudo-divergence-free element free Galerkin method for incompressible fluid flow, Comput. Methods Appl. Mech. Engrg., 193, 12-14, 1119-1136, 2004 · Zbl 1060.76626 |
| [27] | Jackson, C. P., A finite-element study of the onset of vortex shedding in flow past variously shaped bodies, J. Fluid Mech., 182, 23-45, 1987 · Zbl 0639.76041 |
| [28] | Kawahara, M.; Okamoto, T., Finite element analysis of steady flow of viscous fluid using stream function, Proc. Jpn. Soc. Civ. Eng., 1976, 247, 123-135, 1976 |
| [29] | Krzeminski, S. K.; Smialek, M.; Wlodarczyk, M., Finite element approximation of biharmonic mathematical model for MHD flow using/spl Psi/-an approach, IEEE Trans. Magn., 36, 4, 1313-1318, 2000 |
| [30] | Kupferman, R., A central-difference scheme for a pure stream function formulation of incompressible viscous flow, SIAM J. Sci. Comput., 23, 1, 1-18, 2001 · Zbl 0995.76060 |
| [31] | Lashckarbolok, M.; Jabbari, E., Collocated discrete least squares (CDLS) meshless method for the stream function-vorticity formulation of 2D incompressible Navier-Stokes equations, Sci. Iranica, 19, 6, 1422-1430, 2012 |
| [32] | Li, X., Element-free Galerkin analysis of Stokes problems using the reproducing kernel gradient smoothing integration, J. Sci. Comput., 96, 2, 43, 2023 · Zbl 07708344 |
| [33] | Li, X., A stabilized element-free Galerkin method for the advection-diffusion-reaction problem, Appl. Math. Lett., 146, Article 108831 pp., 2023 · Zbl 1522.65219 |
| [34] | Lin, H.; Atluri, S. N., The meshless local Petrov-Galerkin (MLPG) method for solving incompressible Navier-Stokes equations, CMES- Comput. Model. Eng. Sci., 2, 2, 117-142, 2001 |
| [35] | Liu, G.-R.; Gu, Y.-T., An Introduction to Meshfree Methods and Their Programming, 2005, Springer Science & Business Media |
| [36] | Lu, Y.; Hu, A. K.; Liu, Y. C.; Han, C. S., A meshless method based on moving least squares for the simulation of free surface flows, J. Zhejiang Univ.-Sci. A, 17, 2, 130-143, 2016 |
| [37] | Medale, M.; Cochelin, B., High performance computations of steady-state bifurcations in 3D incompressible fluid flows by asymptotic numerical method, J. Comput. Phys., 299, 581-596, 2015 · Zbl 1351.76018 |
| [38] | Mesmoudi, S.; Askour, O.; Rammane, M.; Bourihane, O.; Tri, A.; Braikat, B., Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams, Internat. J. Numer. Methods Engrg., 123, 24, 6111-6126, 2022 · Zbl 1531.74082 |
| [39] | Mizushima, J.; Okamoto, H.; Yamaguchi, H., Stability of flow in a channel with a suddenly expanded part, Phys. Fluids, 8, 11, 2933-2942, 1996 · Zbl 1027.76562 |
| [40] | Mohammadi, M. H., Stabilized meshless local Petrov-Galerkin (MLPG) method for incompressible viscous fluid flows, CMES Comput. Model. Eng. Sci., 29, 2, 75-94, 2008 · Zbl 1232.76028 |
| [41] | Mozolevski, I.; Süli, E.; Bösing, P. R., Discontinuous Galerkin finite element approximation of the two-dimensional Navier-Stokes equations in stream-function formulation, Commun. Numer. Methods. Eng., 23, 6, 447-459, 2007 · Zbl 1262.76053 |
| [42] | Nath, D.; Kalra, M. S.; Munshi, P., One-stage method of fundamental and particular solutions (MFS-MPS) for the steady Navier-Stokes equations in a lid-driven cavity, Eng. Anal. Bound. Elem., 58, 39-47, 2015 · Zbl 1403.76048 |
| [43] | Norberg, U. M., Chapter 8 - The anatomy of the airfoil, (Gudmundsson, S., General Aviation Aircraft Design, 2014, Butterworth-Heinemann: Butterworth-Heinemann Boston), 235-297 |
| [44] | Rammane, M.; Elmhaia, O.; Mesmoudi, S.; Askour, O.; Braikat, B.; Tri, A.; Damil, N., On the use of Hermit-type WLS approximation in a high order continuation method for buckling and wrinkling analysis of von-Kàrmàn plates, Eng. Struct., 278, Article 115498 pp., 2023 |
| [45] | Rammane, M.; Mesmoudi, S.; Tri, A.; Braikat, B.; Damil, N., Solving the incompressible fluid flows by a high-order mesh-free approach, Internat. J. Numer. Methods Fluids, 92, 5, 422-435, 2020 |
| [46] | Rammane, M.; Mesmoudi, S.; Tri, A.; Braikat, B.; Damil, N., Bifurcation points and bifurcated branches in fluids mechanics by high-order mesh-free geometric progression algorithms, Internat. J. Numer. Methods Fluids, 93, 3, 834-852, 2021 |
| [47] | Rammane, M.; Mesmoudi, S.; Tri, A.; Braikat, B.; Damil, N., A dimensionless numerical mesh-free model for the compressible fluid flows, Comput. & Fluids, 221, Article 104845 pp., 2021 · Zbl 1521.76576 |
| [48] | Rammane, M.; Mesmoudi, S.; Tri, A.; Braikat, B.; Damil, N., Mesh-free model for Hopf’s bifurcation points in incompressible fluid flows problems, Int. J. Numer. Methods Fluids, 94, 9, 1566-1581, 2022 |
| [49] | Sedaghatjoo, Z.; Dehghan, M.; Hosseinzadeh, H., Numerical solution of 2D Navier-Stokes equation discretized via boundary elements method and finite difference approximation, Eng. Anal. Bound. Elem., 96, 64-77, 2018 · Zbl 1403.76102 |
| [50] | Sonawane, C. R.; More, Y. B.; Pandey, A. K., Numerical simulation of unsteady channel flow with a moving indentation using solution dependent weighted least squares based gradients calculations over unstructured mesh, Heat Transf. Eng., 43, 3-5, 300-313, 2021 |
| [51] | Wahba, E. M., Iterative solvers and inflow boundary conditions for plane sudden expansion flows, Appl. Math. Model., 31, 11, 2553-2563, 2007 · Zbl 1325.76141 |
| [52] | Weinan, E.; Liu, J. G., Vorticity boundary condition and related issues for finite difference schemes, J. Comput. Phys., 124, 2, 368-382, 1996 · Zbl 0847.76050 |
| [53] | Yang, J.; Potier-Ferry, M.; Hu, H., Solving the stationary Navier-Stokes equations by using Taylor meshless method, Eng. Anal. Bound. Elem., 98, 8-16, 2019 · Zbl 1404.76197 |
| [54] | Zhang, L.; Ouyang, J.; Zhang, X. H., On a two-level element-free Galerkin method for incompressible fluid flow, Appl. Numer. Math., 59, 8, 1894-1904, 2009 · Zbl 1419.76514 |
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