Defect correction method for time-dependent viscoelastic fluid flow

Abstract

A defect correction method for solving the time-dependent viscoelastic fluid flow, aiming at high Weissenberg numbers, is presented. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the residual is considered in the correction step. We show the convergence of the method and derive an error estimate. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.

Keywords:

• viscoelastic fluid flow
• finite element
• time dependent
• defect correction method
• discontinuous Galerkin
• error estimate
• Weissenberg number

2000 AMS Subject Classification :

• 65N30

Acknowledgements

This work was supported by the National Natural Science Foundation of China(10871156) and Jiaoda Foundation(2009xjtujc30). The authors would like to thank Prof J.S. Howell for meaty discussion of program code. The authors also thank the anonymous reviewer and editor for their valuable comments and suggestions that helped to improve the results of the paper.