TY  - EJOU
AU  - An-Vo, D.-A. 
AU  - Mai-Duy, N. 
AU  - Tran-Cong, T. 

TI  - IRBFEs for the numerical solution of steady incompressible flows
T2  - The International Conference on Computational \& Experimental Engineering and Sciences

PY  - 2011
VL  - 16
IS  - 3
SN  - 1933-2815

AB  - In this paper, we develop a control-volume technique based on 2-node integrated-radial-basis-function elements (IRBFEs) for the numerical solution of steady incompressible flows governed by the stream function-vorticity formulation. The fluid domain is discretised by a Cartesian grid from which non-overlapping rectangular control- volumes are formed. Line integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. The convection term is effectively treated by the upwind scheme with deferred correction strategy. Instead of using conventional low-order polynomials, all physical quantities at the interfaces are presently estimated by means of 2-node IRBFEs. Attractive features of the proposed technique include (i) the solution is C2-continuous across the elements and (ii) a wide range of the RBF shape parameter can be used. Numerical results are presented for several two-dimensional benchmark problems defined on rectangular and non-rectangular domains.
KW  - Integrated-radial-basis-function elements
KW  -  Cartesian grids
KW  -  control volume
KW  -  local approximation
KW  -  upwind scheme
KW  -  deferred-correction strategy

DO  - 10.3970/icces.2011.016.087