Body types overview

Parameter value for `body_type`	Description
`none` (default)	No immersed boundary
`center_wall`	Planar static wall centered in y
`double_cylinders_z`	Two concentric cylinders parallel to the z axis
`standing_wave`	Two walls (at y = 0 and y = `Ly_ref`) undergoing a prescribed streamwise standing wave deformation with the same phase
`traveling_wave_x`	Two walls (at y = 0 and y = `Ly_ref`) undergoing a prescribed streamwise traveling wave deformation with the opposite phase

Center wall (`center_wall`)

Field	Value
Parameter value for `body_type`	`center_wall`
`nb`	`nxb` * `nzb`
`body_param_1`	N/A
`body_param_2`	N/A
`body_param_3`	N/A
`body_ramp_up_time` considered?	No

Field	Value
Parameter value for `body_type`	`double_cylinders_z`
`nb`	Computed such that the body-to-grid spacing ratio in the x direction matches that of the z direction, determined by `nzb` and `nz_global`
`body_param_1`	Radius inner cylinder
`body_param_2`	Radius outer cylinder
`body_param_3`	Tangential velocity boundary condition at the inner cylinder
`body_ramp_up_time` considered?	No

Displacement upper wall:

\[ \eta_{U} = b_1 \cos( b_2 t) \sin( 2 \pi b_3 x / L_{x,p}) \]

Displacement lower wall:

\[ \eta_{L} = b_1 \cos( b_2 t) \sin( 2 \pi b_3 x / L_{x,p}) \]

Field	Value
Parameter value for `body_type`	`standing_wave`
`nb`	2 * `nxb` * `nzb`
`body_param_1` (\(b_1\))	Displacement amplitude
`body_param_2` (\(b_2\))	Angular frequency
`body_param_3` (\(b_3\))	Streamwise mode index
`body_ramp_up_time` considered?	No

Displacement upper wall:

\[ \eta_{U} = -\frac{b_1}{b_2 b_3} \sin( b_3 (x - b_2 t)) \]

Displacement lower wall:

\[ \eta_{L} = \frac{b_1}{b_2 b_3} \sin( b_3 (x - b_2 t)) \]

Field	Value
Parameter value for `body_type`	`standing_wave`
`nb`	2 * `nxb` * `nzb`
`body_param_1` (\(b_1\))	Velocity amplitude
`body_param_2` (\(b_2\))	Wave speed
`body_param_3` (\(b_3\))	Streamwise wavenumber
`body_ramp_up_time` considered?	Yes