A numerical study of integrated radial-basis-functions for the pressure-velocity formulation

Thai-Quang, Nha and Mai-Duy, Nam and Tran-Cong, Thanh (2012) A numerical study of integrated radial-basis-functions for the pressure-velocity formulation. In: 7th ICCES Special Symposium on Meshless & Other Novel Computational Methods (ICCES MM 2011), 6-10 Sept 2011, Zonguldak, Turkey.

Abstract

This study is concerned with the development of integrated radial-basis-functions (IRBFs) for the simulation of two-dimensional incompressible viscous flows governed by the pressure-velocity formulation on Cartesian grids. Instead of using low-order polynomial interpolants, global 1D-IRBFs, local 2D-IRBFs and compact local 2D-IRBFs are employed to represent the convection and diffusion terms. Furthermore, two effective treatments for the pressure variable, where Neumann boundary conditions are transformed into Dirichlet ones, are proposed. The first one, named Treatment A, is based on values of the pressure at interior nodes along a grid line and first derivative values of the pressure at two extreme nodes of that grid line; while the second one, named Treatment B, relies on values of the pressure at interior nodes along a grid line together with both first and second derivative values of the pressure at two extreme nodes of that grid line. The performance of proposed method is investigated numerically through the solution of linear (e.g. Poisson equation) and nonlinear (e.g. isothermal lid-driven cavity flow) problems. Numerical results indicate that (i) Treatment B is more accurate than Treatment A; and (ii) A scheme based on compact local 2D-IRBFs approximations with Treatment B yields the best performance in terms of accuracy and rate of convergence.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Other)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2012 Tech Science Press. Conference held 2011, but Proceedings published 2012.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 27 May 2013 01:48
Last Modified: 15 Oct 2014 00:07
Uncontrolled Keywords: local approximation, integrated radial-basis-function, pressure-velocity formulation, lid-driven cavity flow, Neumann boundary condition, Dirichlet boundary condition, Cartesian grid.
Fields of Research : 08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080205 Numerical Computation
URI: http://eprints.usq.edu.au/id/eprint/23202

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