A direct Eulerian GRP scheme for a blood flow model in arteries

Wancheng Sheng, Qinglong Zhang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we propose a direct Eulerian generalized Riemann problem (GRP) scheme for a blood flow model in arteries. It is an extension of the Eulerian GRP scheme, which is developed by Ben-Artzi, Li, and Warnecke [J. Comput. Phys., 218 (2006), pp. 19-43]. By using the Riemann invariants, we diagonalize the blood flow system into a weakly coupled system, which is used to resolve rarefaction waves. We also use the Rankine-Hugoniot condition to resolve the local GRP formulation. We pay special attention to the acoustic case as well as the sonic case. The extension to the two-dimensional case is carefully obtained by using the dimensional splitting technique. We test that the derived GRP scheme is second order accuracy.

Original languageEnglish (US)
Pages (from-to)A1975-A1996
JournalSIAM Journal on Scientific Computing
Issue number3
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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