On the accuracy of the collocation Trefftz method for solving two- and three-dimensional heat equations. (2nd April 2016)

• Record Type: Journal Article
• Authors: Ku, Cheng-Yu; Xiao, Jing-En; Liu, Chih-Yu; Yeih, Weichung
• Is Part Of: Numerical heat transfer. Volume 69:Number 4(2016)
• Page Start: 334
• Page End: 350
• Publication Date: 2016-04-02
• Subjects: Heat -- Transmission -- Measurement -- Periodicals; Mass transfer -- Measurement -- Periodicals; Numerical analysis -- Periodicals; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; 621.4022
• DOI: 10.1080/10407790.2015.1125215
• Languages: English
• ISSNs: 1040-7790

Abstract

ABSTRACT: In this article, the accuracy of the collocation Trefftz method (CTM) for solving two- and three-dimensional heat equations is investigated. The numerical solutions are approximated by superpositioning T-complete functions formulated using cylindrical harmonics. To avoid the ill-conditioning of the CTM, the characteristic lengths and the multiple-scale Trefftz method are adopted. The results reveal that for two-dimensional problems, the CTM can provide highly accurate numerical solutions, with the accuracy increasing with the order of the terms. For three-dimensional problems, highly accurate numerical solutions can be obtained using a certain order of terms, where the order is determined by performing an accuracy assessment.