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An energy stable numerical scheme and its theoretical analysis for Oldroyd-B viscoelastic flow problem

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  • Hu, Xiaolin
  • Gao, Puyang
  • Tu, Changyu

Abstract

In this paper, we provide a comprehensive theoretical analysis for the stabilized numerical scheme LCR-DEVSS-G of the Oldroyd-B viscoelastic fluid flow problem. Unconditional energy stability at the fully discrete level is established for the scheme combining the logarithmic conformation representation (LCR) of the Oldroyd-B model and the Discrete Elastic-Viscous Split-Stress Gradient (DEVSS-G) method. Using energy estimates and Brouwer’s fixed-point theorem, we have proven both the existence and uniqueness of the scheme’s numerical solution, as well as its optimal error estimate. Finally, we conducted numerical experiments, such as the Poiseuille flow and lid-driven cavity, to demonstrate the effectiveness of the proposed scheme and to validate the theoretical analysis.

Suggested Citation

  • Hu, Xiaolin & Gao, Puyang & Tu, Changyu, 2026. "An energy stable numerical scheme and its theoretical analysis for Oldroyd-B viscoelastic flow problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 645-664.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:645-664
    DOI: 10.1016/j.matcom.2026.02.028
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