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Peer-reviewedCC BY 4.0IMA Journal of Numerical Analysis

Convergence of a relaxation method for the approximation of time dependent viscoplastic flow

  • François Bouchut
  • Robert Eymard
  • D Maltese
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Abstract

We propose and analyse a new numerical scheme for the approximation of the flow of time dependent viscoplastic fluids with general potentials. A major advantage of this scheme, based on the relaxation of the nonlinearity, is that it only requires the resolution of one linear system per timestep. Moreover it satisfies the balance of the conserved quantity, and it is proved to converge to the solution of the continuous problem. This behaviour is illustrated by the comparison of numerical solutions with analytical ones.

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Cite

BibTeXRIS
BibTeX
@article{bouchut2026convergence,
  title = {{Convergence of a relaxation method for the approximation of time dependent viscoplastic flow}},
  author = {François Bouchut and Robert Eymard and D Maltese},
  journal = {IMA Journal of Numerical Analysis},
  year = {2026},
  month = sep,
  url = {https://univ-eiffel.hal.science/hal-05693817v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Convergence of a relaxation method for the approximation of time dependent viscoplastic flow
AU  - François Bouchut
AU  - Robert Eymard
AU  - D Maltese
PY  - 2026
DA  - 2026/09/11
JO  - IMA Journal of Numerical Analysis
UR  - https://univ-eiffel.hal.science/hal-05693817v2
AB  - We propose and analyse a new numerical scheme for the approximation of the flow of time dependent viscoplastic fluids with general potentials. A major advantage of this scheme, based on the relaxation of the nonlinearity, is that it only requires the resolution of one linear system per timestep. Moreover it satisfies the balance of the conserved quantity, and it is proved to converge to the solution of the continuous problem. This behaviour is illustrated by the comparison of numerical solutions with analytical ones.
SN  - 0272-4979
SN  - 1464-3642
ER  -