Jufeng Wang¹, Yong Wu¹, Ying Xu¹, Fengxin Sun^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 341-356, 2023, DOI:10.32604/cmes.2022.023140

Abstract By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the… More >

Kamil Khan¹, Arshed Ali^1,*, Fazal-i-Haq², Iltaf Hussain³, Nudrat Amir⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 673-692, 2021, DOI:10.32604/cmes.2021.012730

Abstract This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used for interpolation in both methods. The first method is CTBS based collocation method which reduces the PIDE to an algebraic tridiagonal system of linear equations. The other method is CTBS based differential quadrature method which converts the PIDE to a system of ODEs by computing spatial derivatives as weighted sum of function values. An efficient tridiagonal solver is used for the solution of the linear system obtained in the first method… More >

Shengyang Feng^1,2,3,*, Dongbo Xiong⁴, Guojie Chen⁵, Yu Cui¹, Puxin Chen¹

FDMP-Fluid Dynamics & Materials Processing, Vol.16, No.3, pp. 651-663, 2020, DOI:10.32604/fdmp.2020.07981

Abstract Convection and diffusion are the main factors affecting radon migration. In this paper, a coupled diffusion-convection radon migration model is presented taking into account turbulence effects. In particular, the migration of radon is simulated in the framework of the k-ε turbulence model. The model equations are solved in a complex 3D domain by the finite element method (FEM). Special attention is paid to the case study about radon migration in an abandoned air defense shelter (AADS). The results show that air convection in a confined space has a great influence on the radon migration and the radon concentration is inversely… 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 >

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 >

Ahmad Shirzadi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 45-64, 2012, DOI:10.3970/cmes.2012.085.045

Abstract This paper presents a meshless method based on the meshless local integral equation (LIE) method for solving the two-dimensional diffusion and diffusion-convection equations subject to a non-local condition. Suitable finite difference scheme is used to eliminate the time dependence of the problem. A weak formulation on local subdomains with employing the fundamental solution of the Laplace equation as test function transforms the resultant elliptic type equations into local integral equations. Then, the Moving Least Squares (MLS) approximation is employed for discretizing spatial variables. Two illustrative examples with exact solutions being used as benchmark solutions are presented to show the efficiency… More >

Yiming Chen, Mingxu Yi, Chen Chen, Chunxiao Yu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 639-654, 2012, DOI:10.3970/cmes.2012.083.639

Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of space-time fractional convection-diffusion equation with variable coefficients. This method combines the definition of fractional derivatives with some properties of Bernstein polynomials and are dispersed the coefficients efficaciously. The main characteristic behind this method is that the original problem is translated into a Sylvester equation. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples show that the method is effective. More >

Xiao Zhao¹, Haitian Yang^1,2, Qiang Gao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.2, pp. 139-160, 2011, DOI:10.3970/cmes.2011.074.139

Abstract A piecewised adaptive algorithm in the time domain is presented to solve the transient convection-diffusion heat transfer problem. By expanding all variables at a time interval, an initial and boundary value problem is decoupled into a series of recursive boundary value problems which can be solved by FEM or other well developed numerical schemes to deal with boundary value problems. A steady computing accuracy can be adaptively maintained via the power increase of the expansion, particularly when the step size varies in the whole computing process. Additionally for the nonlinear cases, there is no requirement of iteration and additional assumption… More >