[Time for "Follow The Logic" with our host: Minamimoto Sho! Bug to insect to butterfly to...]
The governing equation of the incompressible flow is the Navier–Stokes equation: ∂u∂t+(u⋅∇)u=−∇pρair+ν∇2u+fIB, (1a) ∇⋅u=0, (1b) where u is the velocity of the flow, and p is the pressure. The interactions between the flow and the butterfly are calculated by the immersed boundary method. The interactions are introduced as the boundary force fIB . The values of the air properties are adopted from those at 25 °C: the density ρ air = 1.184 kg/m 3 and the kinematic viscosity ν air = 1.54 × 10 −5 m 2/s.
The direction of the main stream is taken as the positive x direction, the vertically upward direction as the positive y direction, and the horizontal direction as the z direction. The directions are expressed by the Cartesian unit vectors ex , ey , and ez. The boundary conditions of the flows are as follows: The velocity is constant on the inflow boundary plane: u=u0ex . The Sommerfeld condition is employed as the outflow condition. The boundary condition of the pressure is the Neumann boundary condition ∂ p/∂ x = 0 on both inflow and outflow plane. The streamwise length of the computational domain is L x = 5 × 10 −1 m, which is approximately 18 times as long as the mean wing-chord length. The periodic boundary condition is employed for the transverse boundaries. The transverse length of the computational domain is L y = L z = 2.5 × 10 −1 m, which is approximately 5 times as long as the wing-tip length. The results are not affected by the values of L x , L y , and L z.
[To pretty much anyone but a mathematician or a physicist it probably mostly comes across as BLAH BLAH NUMBER BLAH NUMBER NUMBER SPAZ FLAIL BLERG.]
[[This be ripped straight outta this article. All things correct are because of the people who wrote the article, anything messed up is because I am sooooo not a mathematician.]]
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The governing equation of the incompressible flow is the Navier–Stokes equation:
∂u∂t+(u⋅∇)u=−∇pρair+ν∇2u+fIB,
(1a)
∇⋅u=0,
(1b)
where u is the velocity of the flow, and p is the pressure. The interactions between the flow and the butterfly are calculated by the immersed boundary method. The interactions are introduced as the boundary force fIB . The values of the air properties are adopted from those at 25 °C: the density ρ air = 1.184 kg/m 3 and the kinematic viscosity ν air = 1.54 × 10 −5 m 2/s.
The direction of the main stream is taken as the positive x direction, the vertically upward direction as the positive y direction, and the horizontal direction as the z direction. The directions are expressed by the Cartesian unit vectors ex , ey , and ez. The boundary conditions of the flows are as follows: The velocity is constant on the inflow boundary plane: u=u0ex . The Sommerfeld condition is employed as the outflow condition. The boundary condition of the pressure is the Neumann boundary condition ∂ p/∂ x = 0 on both inflow and outflow plane. The streamwise length of the computational domain is L x = 5 × 10 −1 m, which is approximately 18 times as long as the mean wing-chord length. The periodic boundary condition is employed for the transverse boundaries. The transverse length of the computational domain is L y = L z = 2.5 × 10 −1 m, which is approximately 5 times as long as the wing-tip length. The results are not affected by the values of L x , L y , and L z.
[To pretty much anyone but a mathematician or a physicist it probably mostly comes across as BLAH BLAH NUMBER BLAH NUMBER NUMBER SPAZ FLAIL BLERG.]
[[This be ripped straight outta this article. All things correct are because of the people who wrote the article, anything messed up is because I am sooooo not a mathematician.]]