Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
The splitting-based semi-implicit finite-difference schemes for simulation of blood flow in arteries. / Кривовичев, Герасим Владимирович.
в: Computers and Fluids, Том 266, 106049, 15.11.2023.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - The splitting-based semi-implicit finite-difference schemes for simulation of blood flow in arteries
AU - Кривовичев, Герасим Владимирович
PY - 2023/11/15
Y1 - 2023/11/15
N2 - This paper is devoted to construction and analysis of splitting-based finite-difference schemes for simulation of blood flow in applications of one-dimensional models. Proposed schemes are constructed for inviscid and viscid models of blood. The proposed approach is based on the modification of averaged incompressibility condition, rewritten for the square root of a cross-sectional area. It is approximated by an absolutely stable scheme with a skew-symmetric operator. The constructed schemes can be classified as semi-implicit. The stability of proposed schemes is analyzed by the method of energy inequalities. Sufficient stability conditions are obtained. For the problems with analytical solutions, it is demonstrated that a second-order convergence rate is achieved in practice. The proposed schemes are compared with the widely used explicit finite-difference schemes, such as Lax–Wendroff, Lax–Friedrichs and McCormack schemes. The benchmark problems for simulation of flows in the following vascular systems are considered: human carotid artery, human aorta with bifurcation, vessel with bifurcation and absorbing outflow conditions, and networks with 31, 63, and 127 vessels. It is demonstrated that the computations based on the splitting-based semi-implicit schemes can be performed much faster than for the explicit schemes with close values of relative errors.
AB - This paper is devoted to construction and analysis of splitting-based finite-difference schemes for simulation of blood flow in applications of one-dimensional models. Proposed schemes are constructed for inviscid and viscid models of blood. The proposed approach is based on the modification of averaged incompressibility condition, rewritten for the square root of a cross-sectional area. It is approximated by an absolutely stable scheme with a skew-symmetric operator. The constructed schemes can be classified as semi-implicit. The stability of proposed schemes is analyzed by the method of energy inequalities. Sufficient stability conditions are obtained. For the problems with analytical solutions, it is demonstrated that a second-order convergence rate is achieved in practice. The proposed schemes are compared with the widely used explicit finite-difference schemes, such as Lax–Wendroff, Lax–Friedrichs and McCormack schemes. The benchmark problems for simulation of flows in the following vascular systems are considered: human carotid artery, human aorta with bifurcation, vessel with bifurcation and absorbing outflow conditions, and networks with 31, 63, and 127 vessels. It is demonstrated that the computations based on the splitting-based semi-implicit schemes can be performed much faster than for the explicit schemes with close values of relative errors.
KW - Blood flow
KW - Finite-difference methods
KW - One-dimensional model
KW - Splitting
UR - https://www.mendeley.com/catalogue/e58aebda-3741-31e8-9b05-072453d9a069/
U2 - 10.1016/j.compfluid.2023.106049
DO - 10.1016/j.compfluid.2023.106049
M3 - Article
VL - 266
JO - Computers and Fluids
JF - Computers and Fluids
SN - 0045-7930
M1 - 106049
ER -
ID: 110598611