TITLE:
A New Two-Dimensional Blood Flow Model and Its RKDG Approximation
AUTHORS:
Yolhan Mannes, Mehmet Ersoy, Ömer Faruk Eker, Aimed Ajroud
KEYWORDS:
Blood Flow, Asymptotic Analysis, Thin-Artery Assumption, Energy Consistency, RKDG Method, Aneurysm
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
18,
2025
ABSTRACT: We propose a new two-dimensional blood flow reduced model taking into account of complex artery geometry as in the case of severe aneurysm. We derive the model from the three-dimensional Navier-Stokes equations written in a curvilinear coordinate system under the thin-artery assumption, with boundary conditions including wall tissue deformation. We show that the model is energetically consistent with the full Navier-Stokes problem. This model, obtained via radial averaging, is, up to our knowledge, the first one. It has the advantage of being more accurate than the classical one-dimensional models and being solved in a reasonable time in comparison with the Navier-Stokes models. To this purpose, we use a Runge-Kutta Discontinuous Galerkin (RKDG) method to solve the two-dimensional problem. We end the paper with several numerical test cases to show the efficiency and robustness of the numerical model, and in particular, we show the limit of the one-dimensional models in the case of a severe aneurysm.