Table 2.

Boundary conditions for Navier–Stokes and diffusion–convection equations

Navier–Stokes equation		Diffusion–convection equation
(1) Inlet BC	U = 2Umean · [1−(s/so)2]	(1) Inlet BC	C = Co
(lumen flow velocity)	Vi = −U·n	(constant Co)
(2) Symmetric BC	n·Vi = 0, t · [−pI + µ(∇Vi + (∇Vi)T] = 0	(2) Symmetric BC	n · n = 0, N = −D · ∇C + CVi
(3) Slip BC	n·Vi = 0, t · [−pI + µ(∇Vi + (∇Vi)T] = 0	(3) Insulation BC	n · n = 0, N = −D · ∇C + CVi
(4) Flux BC	Vi = -Jv · n, Jv = Jvo(1 − Ci/(Ci + Kd))	(4) Insulation BC	n · n = 0, N = −D · ∇C + CVi
(5) Outlet BC	[µ(∇Vi + (∇Vi)T]n = 0, p = p0	(5) Outlet BC	n·(−D∇C) = 0
(no viscous stress)		(convective flux)

BC, boundary condition; n, surface normal vector; I, unit vector; ∇, gradient operator. Other variables are defined in the main text.