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We address a simplified time-dependent parabolic problem that arises when modeling both viscoelastic fluids and elastic solids in a unified framework. A priori estimates are obtained for the continuous problem. Then implicit and semi-explicit (EVSS) time discretizations are considered. Stability estimates are obtained for the time-discretized problems. Numerical experiments show that appropriate convergence orders are obtained and that the implicit scheme is more accurate.

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Numerical Analysis of a Simplified Unified Model for Viscoelastic Fluids and Elastic Solids

  • 会议论文

  • 发表日期：

    2025年

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  • Alexandre Caboussat,
  • Léo Diserens,
  • Marco Picasso

摘要

We address a simplified time-dependent parabolic problem that arises when modeling both viscoelastic fluids and elastic solids in a unified framework. A priori estimates are obtained for the continuous problem. Then implicit and semi-explicit (EVSS) time discretizations are considered. Stability estimates are obtained for the time-discretized problems. Numerical experiments show that appropriate convergence orders are obtained and that the implicit scheme is more accurate.