Problems

gridstep(::CartesianGrid)

The spacing between grid vertices.

gridstep(::MultiDomainGrid, level=1)

Grid step on the levelth multi domain level.

gridsize(grid::CartesianGrid, pts::GridPoints=GridVertices())

Returns the dimensions of an array of points on the grid.

gridsize(grid::MultiDomainGrid, pts::GridPoints=GridVertices(), levels=:)

The dimensions of the multi domain grid.

extents(::CartesianGrid) -> ((xmin, xmax), (ymin, ymax))

Minimum and maximum coordinates of the grid.

coords(grid::CartesianGrid, pts::GridPoints=GridVertices())

Returns a tuple of ranges (x, y) such that (x[i], y[j]) is the coordinate of the point at index (i, j).

coords(grid::MultiDomainGrid, pts::GridPoints=GridVertices(), levels=:)

Return the coordinates of each CartesianGrid subdomain in levels.

coords(grid, func, ...)

Coordinates of the quantity func on grid. func can be one of the following (or the in-place ! versions):

• x_velocity
• y_velocity
• vorticity

fluid_grid(; [h], xlims, ylims, nlevel)

A cartesian grid with step h, limits xlims and ylims, and nlevel total grids that expand outward. Each grid has the same center point, and grid step h * 2 ^ (level - 1) for level in 1:nlevel. If h is included, return a MultiDomainGrid. Otherwise, return a MultiDomainExtents and the grid step will be automatically computed when passed to Fluid.

CartesianGrid(h, xlims, ylims)
CartesianGrid(; h, xlims, ylims)

A Cartesian grid with grid step h.

MultiDomainGrid(; h, xlims, ylims, nlevel)

Multiple CartesianGrids with different scales, centered at the same point.

See also fluid_grid.

MultiDomainExtents(; xlims, ylims, nlevel)

The region defined by a MultiDomainGrid, without the grid step.

See also fluid_grid.

subdomain(grid::MultiDomainGrid, level) :: CartesianGrid

Return the levelth multi domain level of grid.

GridMotion

The motion of the fluid discretization relative to the global frame in which the freestream velocity is expressed. Can be one of:

• StaticGrid
• MovingGrid

StaticGrid() :: GridMotion

A grid that is static in the global frame.

MovingGrid(f) :: GridMotion

A grid that moves in global frame. f(t) should return a GridVelocity that expresses the current motion of the grid.

GridVelocity(; center, vel, angle, angular_vel)

The current motion and orientation of the grid relative to the global frame.

Keywords

• center: The center of rotation.
• vel: The grid's velocity in the global frame at the center of rotation.
• angle: The grid's orientation relative to the global frame in radians.
• angular_vel: The time rate of change of angle.

Fluid(; grid, Re, freestream_vel, [grid_motion])

Keywords

• grid::Union{MultiDomainGrid,MultiDomainExtents}: The discretization of the fluid. See fluid_grid.
• Re: Reynolds number.
• freestream_vel(t) -> (vx, vy): Freestream velocity as a function of time.
• grid_motion::GridMotion: Whether the grid is moving relative to the global frame.

n_panels(x)

The number of panels in a thing.

Panels(x::AbstractMatrix, ds::AbstractVector)

The positions xb and lengths ds of panels that influence the fluid. xb has shape (n, 2) and ds has length n.

PanelState(; xb::AbstractMatrix, ds::AbstractVector, ub::AbstractMatrix)

The positions xb, lengths ds, and velocities ub of panels that influence the fluid. xb and ub have shape (n, 2) and ds has length n.

AbstractBody

A body that can be immersed in the fluid.

PresetBody <: AbstractBody

A body that is not influenced by the fluid.

Bodies(; bodies::AbstractBody...)

A group of bodies. Keyword arguments specify bodies by their name.

PanelSection

Specifies a subsection of the panels in Bodies.

section_body(section::PanelSection)

The AbstractBody of a section.

panel_range(bodies::Bodies, body::Symbol)
panel_range(section::PanelSection)

The index range in the panels of the given body.

bodypanels(body::AbstractBody)

The Panels of a body's reference state.

StaticBody(panels::Panels) :: PresetBody

A body that is fixed in place at panels.

RigidBodyTransform(pos, vel, angle, angular_vel)
RigidBodyTransform(; pos, vel, angle, angular_vel)

The transformation of a rigid body at a point in time. Relative to the global frame, the rigid body is at position (x, y) = pos, traveling at velocity (vx, vy) = vel, oriented at angle angle, and rotating at rate angular_vel.

MovingRigidBody(motion, panels::Panels) :: PresetBody

A non-deforming body with displacement and rotation over time. With zero displacement and zero angle, the body is at panels. motion(t) is the RigidBodyTransform of the body at time t.

timestep(prob::Problem)
timestep(scheme::AbstractScheme)

The time between consecutive time steps.

AbstractScheme

A time-stepping scheme.

default_scheme([T,] grid; Umax, [cfl])

A default AbstractScheme to hit a target cfl number.

Arguments

• T::Type{<:AbstractScheme}: The type of scheme to return.
• grid::Union{CartesianGrid,MultiDomainGrid}: The discretization of the fluid.
• Umax: The maximum fluid velocity relative to the discretization.
• cfl: Target CFL number.

CNAB(; dt, n=2)

An n-step Crank-Nicolson/Adams-Bashforth timestepping scheme with time step dt.

Problem(; fluid::Fluid, bodies::Bodies, scheme::AbstractScheme)
Problem(fluid::Fluid, bodies::Bodies, scheme::AbstractScheme)

A description of the immersed boundary problem to solve.

State(prob::Problem; t0=0.0)

The state of the prob system at a certain time step. t0 specifies the time at state.index == 1.

x_velocity(state, [levels])

Return the x velocity array of state on subdomain levels.

y_velocity(state, [levels])

Return the y velocity array of state on subdomain levels.

vorticity(state, [levels])

Return the vorticity array of state on subdomain levels.

boundary_pos(state)
boundary_pos(state, inds)
boundary_pos(state, body::Symbol)

Return the positions of each panel point. In the first form, return all of the points. In the second form, return the points at indices inds. In the last form, return the points for the body named body.

boundary_len(state)
boundary_len(state, inds)
boundary_len(state, body::Symbol)

Return the lengths of each panel. See boundary_pos for the meaning of the parameters.

boundary_vel(state)
boundary_vel(state, inds)
boundary_vel(state, body::Symbol)

Return the velocities of each panel. See boundary_pos for the meaning of the parameters.

boundary_(state)
boundary_force(state, inds)
boundary_force(state, body::Symbol)

Return the force on each panel by the fluid. See boundary_pos for the meaning of the parameters.

boundary_total_force(state)
boundary_total_force(state, inds)
boundary_total_force(state, body::Symbol)

The total [x, y] force. See boundary_pos for the meaning of the parameters.