A quadratic b-spline based isogeometric analysis of transient wave propagation problems with implicit time integration method

Weibin Wen, Shengyu Duan, Kai Wei*, Yongbin Ma, Daining Fang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

A uniform quadratic b-spline isogeometric element is exclusively considered for wave propagation problem with the use of desirable implicit time integration scheme. A generalized numerical algorithm is proposed for dispersion analysis of one-dimensional (1-D) and two-dimensional (2-D) wave propagation problems where the quantified influence of the defined CFL number on wave velocity error is analyzed and obtained. Meanwhile, the optimal CFL (Courant–Friedrichs–Lewy) number for the proposed 1-D and 2-D problems is suggested. Four representative numerical simulations confirm the effectiveness of the proposed method and the correctness of dispersion analysis when appropriate spatial element size and time increment are adopted. The desirable computation efficiency of the proposed isogeometric method was confirmed by conducting time cost and calculation accuracy analysis of a 2-D numerical example where the referred FEM was also tested for comparison.

Original languageEnglish
Pages (from-to)115-131
Number of pages17
JournalApplied Mathematical Modelling
Volume59
DOIs
Publication statusPublished - Jul 2018

Keywords

  • Isogeometric analysis
  • Numerical dissipation
  • Time integration
  • Wave propagation
  • b-spline

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