Direct collocation with reproducing kernel approximation for two-phase coupling system in a porous enclosure

Judy P. Yang*, Yi Shan Liao

*此作品的通信作者

研究成果: Article同行評審

5 引文 斯高帕斯(Scopus)

摘要

The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated porous media involves phase coupling, the resulting system is highly nonlinear in nature. To this end, the local approximation is adopted in conjunction with Newton-Raphson method. Nevertheless, to unveil the performance of the method in the nonlinear analysis, only single thermal natural convection is of major concern herein. A unit square is designated as the model problem to investigate the parameters in the system related to the convergence; several benchmark problems are used to verify the accuracy of the approximation, in which the stability of the method is demonstrated by considering various initial conditions, disturbance of discretization, inclination, aspect ratio, and reproducing kernel support size. It is shown that a larger support size can be flexible in approximating highly irregular discretized problems. The derivation of explicit operators with two-phase variables in solving the nonlinear system using the direct collocation is carried out in detail.

原文English
文章編號897
期刊Mathematics
9
發行號8
DOIs
出版狀態Published - 2 4月 2021

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