D. Ho-Minh¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.3, pp. 217-252, 2010, DOI:10.3970/cmes.2010.070.217

Abstract In this paper, one-dimensional integrated radial-basis-function networks (1D-IRBFNs) are introduced into the Galerkin and point-collocation formulations to simulate viscoelastic flows. The computational domain is represented by a Cartesian grid and IRBFNs, which are constructed through integration, are employed on each grid line to approximate the field variables including stresses in the streamfunction-vorticity formulation. Two types of fluid, namely Oldroyd-B and CEF models, are considered. The proposed methods are validated through the numerical simulation of several benchmark test problems including flows in a rectangular duct and in a corrugated tube. Numerical results show that accurate results are obtained using relatively-coarse grids. More >

N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 213-238, 2009, DOI:10.3970/cmes.2009.051.213

Abstract This paper reports a new numerical scheme based on Cartesian grids and local integrated radial-basis-function networks (IRBFNs) for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Linear (e.g. heat flow) and nonlinear (e.g. lid-driven triangular-cavity fluid flow) problems are considered. Numerical results indicate that the local IRBFN CV scheme outperforms the local IRBFN point-collocation scheme regarding accuracy. Moreover, the former… More >

B. M. Pasquim¹, V. C. Mariani²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 113-132, 2008, DOI:10.3970/cmes.2008.035.113

Abstract This study presents a Cartesian grid method and its application to solve a steady flow in a lid-driven triangular two-dimensional cavity. The evolution of stream function and vorticity inside a triangular lid-driven cavity, when the Reynolds number changes from 1 to 6000, is presented. For space discretization on the interior of triangular cavity orthogonal Cartesian grid is used. Then, using this grid, trapezoidal volumes appear in the interface between solid and fluid. For a suitable treatment of these volumes the Eulerian-Lagrangian methodology is used. The Navier-Stokes equations are solved numerically using finite-volume method. On the basis of the numerical studies… More >

N. Thai-Quang¹, K. Le-Cao¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 528-558, 2012, DOI:10.3970/cmes.2012.084.528

Abstract This study is concerned with the development of integrated radial-basis-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… More >

D. Ngo-Cong, N. Mai-Duy, W. Karunasena, T. Tran-Cong

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.083.459

Abstract The partition of unity method is employed to incorporate the moving least square (MLS) and one dimensional-integrated radial basis function (1D-IRBFN) techniques in a new approach, namely local MLS-1D-IRBFN or LMLS-1D-IRBFN. This approach leads to sparse system matrices and offers a high level of accuracy as in the case of 1D-IRBFN method. A new numerical procedure based on the 1D-IRBFN method and LMLS-1D-IRBFN approach is presented for a solution of fluid-structure interaction (FSI) problems. A combination of Chorin's method and pseudo-time subiterative technique is presented for a transient solution of 2-D incompressible viscous Navier-Stokes equations in terms of primitive variables.… More >

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 275-310, 2012, DOI:10.3970/cmes.2012.083.275

Abstract In this paper, natural convection flows in concentric and eccentric annuli are studied using a new numerical method, namely local moving least square - one dimensional integrated radial basis function networks (LMLS-1D-IRBFN). The partition of unity method is used to incorporate the moving least square (MLS) and one dimensional-integrated radial basis function (1D-IRBFN) techniques in an approach that leads to sparse system matrices and offers a high level of accuracy as in the case of 1D-IRBFN method. The present method possesses a Kronecker-Delta function property which helps impose the essential boundary condition in an exact manner. The method is first… More >

D.-A. An-Vo¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.2, pp. 141-178, 2011, DOI:10.3970/cmes.2011.080.141

Abstract In this paper, 2-node integrated radial basis function elements (IRBFEs) [CMES, vol.72, no.4, pp.299-334, 2011] are further developed for the simulation of incompressible viscous flows in two dimensions. Emphasis is placed on (i) the incorporation of C²-continuous 2-node IRBFEs into the subregion and point collocation frameworks for the discretisation of the stream function-vorticity formulation on Cartesian grids; and (ii) the development of high order upwind schemes based on 2-node IRBFEs for the case of convection-dominant flows. High levels of accuracy and efficiency of the present methods are demonstrated by solutions of several benchmark problems defined on rectangular and non-rectangular domains. More >

Bruno Manoel Pasquim¹, Viviana Cocco Mariani¹

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.1, pp. 63-82, 2011, DOI:10.3970/cmes.2011.079.063

Abstract The main aim of this study was to evaluate the capacity of a Eulerian-Lagrangian methodology (ELAFINT) to accurately deal with incompressible viscous steady flow in a domain with corners and curved boundaries. Thus, a two-dimensional lid-driven cavity with an irregular bottom was selected. The equations that govern the flow are discretized using the finite-volume method with a Cartesian grid. The evolution of the velocity fields, stream function and vorticity in the irregular cavity when the Reynolds number increases from 500 to 6000 is captured by the method under investigation. The results show that with an increase in the Reynolds number… More >

D.-A. An-Vo¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 299-336, 2011, DOI:10.3970/cmes.2011.072.299

Abstract This paper presents a new control-volume discretisation method, based on Cartesian grids and integrated-radial-basis-function elements (IRBFEs), for the solution of second-order elliptic problems in one and two dimensions. The governing equation is discretised by means of the control-volume formulation and the division of the problem domain into non-overlapping control volumes is based on a Cartesian grid. Salient features of the present method include (i) an element is defined by two adjacent nodes on a grid line, (ii) the IRBF approximations on each element are constructed using only two RBF centres (a smallest RBF set) associated with the two nodes of… More >

B. Obradovic¹, M. Radisic², G. Vunjak-Novakovic³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.3, pp. 189-202, 2007, DOI:10.3970/fdmp.2007.003.189

Abstract Efficient transport of oxygen is one of the main requirements in tissue engineering systems in order to avoid cell death in the inner tissue regions and support uniform tissue regeneration. In this paper, we review approaches to design of tissue engineering systems with adequate oxygen delivery for cultivation of cartilage and myocardium, two distinctly different tissue types with respect to the tissue structure and oxygen requirements. Mathematical modeling was used to support experimental results and predict oxygen transport within the cultivated tissues and correlate it to the cell response and tissue properties. More >