Xinyi Guan1, Shaoqiang Tang1,*
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 >
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