B. Šarler¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 185-194, 2005, DOI:10.3970/cmes.2005.007.185

Abstract This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady natural convection benchmark with Prandtl… More >

H. Imtiaz¹, F. M. Mahfouz²

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.3, pp. 171-192, 2015, DOI:10.3970/cmes.2015.108.171

Abstract This paper investigates numerically the conjugate heat transfer in a concentric enclosure that is formed between two concentric cylinders and filled with micropolar fluid. The wall of inner cylinder is considerably thick, while the wall of outer cylinder is very thin. The inner cylinder is heated from inner side through constant heat flux, whereas the outer cylinder is cooled and maintained at constant temperature. The induced buoyancy driven flow and associated conjugate heat transfer are predicted numerically by solving flow and energy governing equations considering a combination of finite difference and Fourier spectral methods. The study investigates the effect of… More >

B. Pekmen^1,2, M. Tezer-Sezgin^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.3, pp. 183-207, 2015, DOI:10.3970/cmes.2015.105.183

Abstract This study proposes the dual reciprocity boundary element (DRBEM) solution for full magnetohydrodynamics (MHD) equations in a lid-driven square cavity. MHD equations are coupled with the heat transfer equation by means of the Boussinesq approximation. Induced magnetic field is also taken into consideration. The governing equations in terms of stream function, temperature, induced magnetic field components, and vorticity are solved employing DRBEM in space together with the implicit backward Euler formula for the time derivatives. The use of DRBEM with linear boundary elements which is a boundary discretization method enables one to obtain small sized linear systems. This makes the… More >

C.M.T. Tien¹, N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.6, pp. 425-469, 2015, DOI:10.3970/cmes.2015.104.425

Abstract In this paper, we propose a three-point coupled compact integrated radial basis function (CCIRBF) approximation scheme for the discretisation of second-order differential problems in one and two dimensions. The CCIRBF employs integrated radial basis functions (IRBFs) to construct the approximations for its first and second derivatives over a three-point stencil in each direction. Nodal values of the first and second derivatives (i.e. extra information), incorporated into approximations by means of the constants of integration, are simultaneously employed to compute the first and second derivatives. The essence of the CCIRBF scheme is to couple the extra information of the nodal first… More >

F. Mechighel^1,2,3, N. Armour⁴, S. Dost⁴, M. Kadja³

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 53-80, 2014, DOI:10.3970/cmes.2014.097.053

Abstract Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The experimental dissolution system was modeled by considering axisymmetric and three-dimensional (3-D) domains. In both cases, the governing equations, namely conservation of mass, momentum balance, energy balance, and solute transport balance, were solved using the Finite Element Method.
Measured concentration profiles and dissolution heights from the experiment samples showed that the application of a… More >

K. Mramor¹, R. Vertnik^2,3, B. Šarler^1,3,4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 327-352, 2013, DOI:10.3970/cmes.2013.092.327

Abstract The purpose of the present paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded subdomains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity with two insulated horizontal and… More >

T.-T. Hoang-Trieu¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.6, pp. 485-516, 2013, DOI:10.3970/cmes.2013.091.485

Abstract In this paper, compact local integrated radial basis function (IRBF) stencils reported in [Mai-Duy and Tran-Cong (2011) Journal of Computational Physics 230(12), 4772-4794] are introduced into the finite-volume / subregion - collocation formulation for the discretisation of second-order differential problems defined on rectangular and non-rectangular domains. The problem domain is simply represented by a Cartesian grid, over which overlapping compact local IRBF stencils are utilised to approximate the field variable and its derivatives. The governing differential equation is integrated over non-overlapping control volumes associated with grid nodes, and the divergence theorem is then applied to convert volume integrals into surface/line… More >

Pratibhamoy Das¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.6, pp. 463-485, 2013, DOI:10.3970/cmes.2013.090.463

Abstract Adaptive mesh generation has become a valuable tool for the improvements of accuracy and efficiency of numerical solutions over fixed number of meshes. This paper gives an interpretation of the concept of equidistribution for singularly perturbed problems to obtain higher-order accuracy. We have used the post-processing Richardson extrapolation technique to improve the accuracy of the parameter uniform computed solution, obtained on a mesh which is adaptively generated by equidistributing a monitor function. Numerical examples demonstrate the high quality behavior of the computed solution. More >

Jinxia Wei¹, Yiming Chen¹, Baofeng Li², Mingxu Yi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.6, pp. 481-495, 2012, DOI:10.3970/cmes.2012.089.481

Abstract In this paper, we present a computational method for solving a class of space-time fractional convection-diffusion equations with variable coefficients which is based on the Haar wavelets operational matrix of fractional order differentiation. Haar wavelets method is used because its computation is sample as it converts the original problem into Sylvester equation. Error analysis is given that shows efficiency of the method. Finally, a numerical example shows the implementation and accuracy of the approach. More >

N. Thai-Quang¹, N. Mai-Duy¹, C.-D Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.3, pp. 189-220, 2012, DOI:10.3970/cmes.2012.089.189

Abstract In this paper, the alternating direction implicit (ADI) method reported in [You(2006)] for the convection-diffusion equation is implemented in the context of compact integrated radial basis function (CIRBF) approximations. The CIRBF approximations are constructed over 3-point stencils, where extra information is incorporated via two forms: only nodal second-order derivative values (Scheme 1), and both nodal first- and second-order derivative values (Scheme 2). The resultant algebraic systems are sparse, especially for Scheme 2 (tridiagonal matrices). Several steady and non-steady problems are considered to verify the present schemes and to compare their accuracy with some other ADI schemes. Numerical results show that… More >