Abstract
This article presents a new method based on meshelss methods in the case of boundary layer. A traditional Finite Elements Method (MEF) is always engaged to calculate many parameters as well as nodes, and elements. This fact, can negatively affect the computational cost. In order to avoid this problem, we propose a new Mesh-Free using only one parameter. The single use of Prandtl equations on “nodes” in Mesh processing can provide a low cost and precision. In addition, the extracted nodes will be modeled using “Radial Basis Function in Finite Differences” (RBF-FD). Simulation of this algorithm is made on Matlab. Numerical results (of dynamic boundary) outperform conventional Mesh-Free methods as well as “Finite Elements Method”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tolstykh, A.I., Shirobokov, D.A.: On using radial basis functions in a finite difference mode with applications to elasticity problems. J. Comput. Mech. 33, 68–79 (2003)
Javed, A., Djidjeli, K., Xing, J.T.: Adaptive shape parameter (ASP) technique for local radial basis functions (RBFs) and their application for solution of Navier-Strokes equations. Int. J. Mech. Aerosp. Inds. Mech. Eng. 7, 771–780 (2013)
Wright, G.B., Fornberg, B.: Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comput. Phys. 212, 99–123 (2006)
Shu, C., Ding, H., Yeo, K.S.: Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations. J. Comput. Methods Appl. Mech. Eng. 192, 941–954 (2003)
Kansa, E.J.: Multiquadrics a scattered data approximation scheme with applications to computational fluid-dynamics II. Solutions to parabolic, hyperbolic and elliptic partial-differential equations. J. Comput. Math. Appl. 19, 147–161 (1990)
Chinchapatnam, P.P., Djidjeli, K., Nair, P.B., Tan, M.: A compact RBF-FD based meshless method for the incompressible Navier-Stokes equations. Proc. Inst. Mech. Eng. Part M: J. Eng. Mar. Environ. 223, 275–290 (2009)
Chandhini, G., Sanyasiraju, Y.V.S.S.: Local RBF-FD solutions for steady convection-diffusion problems. Int. J. Numer. Methods Eng. 72, 352–378 (2007)
Stevens, D., Power, H., Lees, M., Morvan, H.: The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems. J. Comput. Phys. 228, 4606–4624 (2009)
Cecil, T., Qian, J., Osher, S.: Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions. J. Comput. Phys. 196, 327–347 (2004)
Bollig, E.F., Flyer, N., Erlebacher, G.: Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs. J. Comput. Phys. 231, 7133–7151 (2012)
Chinchapatam, P.P.: Radial basis function based meshless methods for fluid flow problems. Thesis, University of Southampton (2006)
Alhuri, Y.: Mesh-free radial basis functions for solving PDES some selected applications to water and coastal systems. Thesis, University of Mohammedia (2011)
Tampango, Y.: Developpement d’une methode sans maillage utilisant les approximations de Taylor. Thesis, University of Lorraine (2012)
Lehto, E.: High order local radial basis function methods for athmospheric flow simulations. Thesis, University of Upsala (2012)
Prandtl, L.: Über Flüssigkeitsbewegungen bei sehr kleiner Reibung. In: 3ème Congrés International dse Mathematiciens. Heiddelberg, pp. 484–491. Teubner, Leipzig (1904)
Ansys: Mohammadia School of Engineers. http://www.emi.ac.ma
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Mnebhi-Loudyi, A., Boudi, E.M., Ouazar, D. (2019). An Adaptative Meshless Method Based on Prandtl’s Equation. In: Ntalianis, K., Vachtsevanos, G., Borne, P., Croitoru, A. (eds) Applied Physics, System Science and Computers III. APSAC 2018. Lecture Notes in Electrical Engineering, vol 574 . Springer, Cham. https://doi.org/10.1007/978-3-030-21507-1_46
Download citation
DOI: https://doi.org/10.1007/978-3-030-21507-1_46
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21506-4
Online ISBN: 978-3-030-21507-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)