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) | ||
| 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.