Governing equations and numerical methods 上式大 SHANGHA <OD model> <ID modet> Closed-loop circulation model U Roles of model 9 P Mass and momentum conservation equations Mass and momentum conservation equations dv1=0,-21 UA >1D model describes dt 0A) ai U pulse wave propagation d№=P-e,R,-P Ly at in the arterial system Pressure-volume relationship Pressure-area relationship P,=V IC P-P。= >oD model closes the 1D model to account for Interior points: systemic hemodynamic Two-Step Lax-Wendroff method behaviors. Fourth-order Runge-Kutta method Coupling Bifurcation conditions: Ghost-point method coupled with the Newton-Raphson method [F.Y.Liang et al.Medical Biological Engineering Computing.2009]<0D model> + <1D model> = Closed-loop circulation model [F.Y. Liang et al. Medical & Biological Engineering & Computing. 2009]  1D model describes pulse wave propagation in the arterial system  0D model closes the 1D model to account for systemic hemodynamic behaviors. Roles of model Governing equations and numerical methods