Mathematical Problems in Engineering

Research Article

On Numerical Solution of the Incompressible Navier-Stokes Equations with Static or Total Pressure Specified on Boundaries

Table 1

Test cases 0 ≤ 𝜃 ≤ 𝜋 , → 𝑢 = ( 𝑢 𝑥 , 𝑢 𝑦 ) , and 𝐻 ( 𝑟 ) = 𝑝 + 𝑣 ( 𝑟 ) 2 / 2 .
CaseFlow-through boundarySolid wall
𝐴 𝐵 ( 𝜃 = 0 ) 𝐶 𝐷 ( 𝜃 = 𝜋 ) 𝐴 𝐷 , 𝐶 𝐵 ( 0 ≤ 𝜃 ≤ 𝜋 )
1 𝑢 𝑥 = 0 , 𝑝 = 𝑓 ( 𝑟 ) 𝑢 𝑥 = 0 , 𝑝 = 𝑓 ( 𝑟 ) + 𝐾 𝜋 𝑢 𝑥 = 𝑢 𝑦 = 0
2 𝑢 𝑥 = 0 , 𝑢 𝑦 = 𝑣 ( 𝑟 ) 𝑢 𝑥 = 0 , 𝑝 = 𝑓 ( 𝑟 ) + 𝐾 𝜋 𝑢 𝑥 = 𝑢 𝑦 = 0
3 𝑢 𝑥 = 0 , 𝑢 𝑦 = 𝑣 ( 𝑟 ) 𝑢 𝑥 = 0 , 𝑝 + 𝑢 2 𝑦 / 2 = 𝐻 ( 𝑟 ) 𝑢 𝑥 = 𝑢 𝑦 = 0
4 𝑢 𝑥 = 0 , 𝑝 = 𝑓 ( 𝑟 ) 𝑢 𝑥 = 0 , 𝑝 + 𝑢 2 𝑦 / 2 = 𝐻 ( 𝑟 ) 𝑢 𝑥 = 𝑢 𝑦 = 0