A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables

Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T. (2012) A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables. CMES: Computer Modeling in Engineering and Sciences, 84 (6). pp. 528-557. ISSN 1526-1492

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This study is concerned with the development of integrated radialbasis- function (IRBF) method for the simulation of two-dimensional steady-state incompressible viscous flows governed by the pressure-velocity formulation on Cartesian grids. Instead of using low-order polynomial interpolants, a high-order compact local IRBF scheme is employed to represent the convection and diffusion terms. Furthermore, an effective boundary treatment for the pressure variable, where Neumann boundary conditions are transformed into Dirichlet ones, is proposed. This transformation is based on global 1D-IRBF approximators using values of the pressure at interior nodes along a grid line and first-order derivative values of the pressure at the two extreme nodes of that grid line. The performance of the proposed scheme is investigated numerically through the solution of several linear (analytic tests including Stokes flows) and non-linear (recirculating cavity flow driven by combined shear & body forces and lid-driven cavity flow) problems. Unlike the global 1D-IRBF scheme, the proposed method leads to a sparse system matrix. Numerical results indicate that (i) the present solutions are more accurate and converge faster with grid refinement in comparison with standard finite-difference results; and (ii) the proposed boundary treatment for the pressure is more effective than conventional direct application of the Neumann boundary condition.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Copyright © 2012 Tech Science Press.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 25 Nov 2012 09:21
Last Modified: 22 Jul 2014 04:41
Uncontrolled Keywords: cartesian grid; compact local stencil; high-order approximation; integrated radial basis function; primitive variables; viscous flow
Fields of Research : 09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
08 Information and Computing Sciences > 0805 Distributed Computing > 080501 Distributed and Grid Systems
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.3970/cmes.2012.084.528
URI: http://eprints.usq.edu.au/id/eprint/21993

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