Xinyi Guan¹, Shaoqiang Tang^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.010869

Abstract Inheriting a convergence difficulty explained by the Kolmogorov N-width [1], the advection-diffusion equation is not effectively solved by the Proper Generalized Decomposition [2] (PGD) method. In this paper, we propose a new strategy: Proper Generalized Decomposition with Coordinate Transformation (CT-PGD). Converting the mixed hyperbolic-parabolic equation to a parabolic one, it resumes the efficiency of convergence for advection-dominant problems. Combining PGD with CT-PGD, we solve advection-diffusion equation by much fewer degrees of freedom, hence improve the efficiency. The advection-dominant regime and diffusion-dominant regime are quantitatively classified by a threshold, computed numerically. Moreover, we find that appropriate More >

Guofei Pang¹, Wen Chen^1,2, K.Y. Sze³

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.4, pp. 299-322, 2014, DOI:10.3970/cmes.2014.097.299

Abstract Space-fractional advection-diffusion equation is a promising tool to describe the solute anomalous transport in underground water, and it has been extended to multi-dimensions with the help of weighted, fractional directional diffusion operator [Benson, Wheatcraft and Meerschaert (2000)]. Due to the nonlocal property of the space-fractional derivative, it is always a challenge to develop an efficient numerical solution method. The present paper extends the polynomialbased differential quadrature and cubature methods to the solution of steady-state spatial fractional advection-diffusion equations on a rectangular domain. An improved differential cubature method is proposed which accelerates the solution process considerably. More >