TY - JOUR
T1 - Advection-Pressure Splitting Schemes for the Equations of Blood Flow. Conservative and Non-Conservative Forms
AU - F. Toro , Eleuterio
AU - Siviglia , Annunziato
AU - Spilimbergo , Alessandra
AU - O. Müller , Lucas
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 223
EP - 259
PY - 2024
DA - 2024/04
SN - 14
DO - http://doi.org/10.4208/eajam.2023-045.090523
UR - https://global-sci.org/intro/article_detail/eajam/23061.html
KW - Blood flow, hyperbolic equations, finite volume method, path-conservative method, TV splitting.
AB - <p style="text-align: justify;">We present a class of simple advection-pressure splitting numerical methods
to solve the blood flow equations in compliant arterial vessels. The schemes are inspired
by the TV flux vector splitting approach for conservative systems, proposed by Toro and
Vázquez [30]. But the reformulated TV-type splitting schemes of this paper have a wider
range of applicability, including systems of equations in non-conservative form. The
spatial differential operator is split into advection terms, which may be in conservative form, from pressure terms in conservative or non-conservative form. Additionally,
unlike the original TV scheme, the reformulated splitting of this paper fully preserves
the continuity equation as part of the pressure system. This last feature is consistent
with zero-dimensional models for blood flow that are based on neglecting the inertial
term in the momentum equation. The schemes are also well suited for systems in which
geometric and biomechanical parameters of the problem vary discontinuously. The splitting schemes of this paper are systematically assessed on a carefully designed suite of
test problems and compared with several existing, mainstream methods. Overall, the
proposed numerical methods perform very satisfactorily and suggest themselves as attractive computational tools for modelling the dynamics of bodily fluids under realistic
conditions.</p>