ImmersedPotentialFlow{Dim, T, M <: GeometricMapping{Dim}, V <: ScalarSplineSpace{Dim, T}, W <: Field{Dim}}

Immersed Galerkin formulation of potential flow. The solution field can be either velocity potential or stream function.

Fields:

• F::M: geometric mapping
• S::V: constrained solution space
• Δ::Partition{Dim, T}: partition
• uʰ::W: solution field
• ūʰ::W: function satisfying Dirichlet boundary condition
• t::Function: traction vector
• ϕ::AlgoimCallLevelSetFunction: level set function

LinearOperator{Dim, T, S <: SparseMatrixCSC{T}, M <: AbstractMatrix{T}, V <: AbstractVector{T}}

Linear operator for ImmersedPotentialFlow model.

Fields:

• C::S: sparse extraction operator
• E::S: sparse extension operator
• K::M: sparse stiffness matrix
• L::S: sparse linear operator Eᵀ Cᵀ K C E
• b::V: right hand side vector

Pressure{Dim, T1, T2 <: Velocity{Dim}}

Pressure mapping for uniform far field flow.

Fields:

• ρ::T1: density
• p::T1: far field pressure
• U::T1: far field velocity magnitude
• velocity::T2: velocity field

abstract type PrimaryField end

Primary field indicator.

PullbackBody{Dim, T <: GeometricMapping{Dim}}

Pullback of bilinear form.

Fields:

• mapping::T: geometric mapping

PullbackBoundary{Dim, T <: GeometricMapping{Dim}}

Pullback of linear form.

Fields:

• mapping::T: geometric mapping
• traction::Function: traction vector
• side::Int: side restriction (side <= 2Dim)

StreamFunction <: PrimaryField

Stream function primary field.

Velocity{Dim, F <: PrimaryField, T1 <: GeometricMapping{Dim}, T2 <: Field{Dim}}

Velocity mapping. Supports potential as velocity potential or stream function.

Fields:

• mapping::T1: geometric mapping
• potential::T2: potential

VelocityPotential <: PrimaryField

Velocity potential primary field.

SparseArrays.sparse(L::LinearOperator)

Get sparse linear operator.

assemble_body(acc::ElementAccessor{Dim}, acc_immersed::ElementAccessor{Dim}, partition::Partition{Dim}, pullback::PullbackBody{Dim}, ϕ::AlgoimCallLevelSetFunction; show_progress::Bool = true)

Assemble unconstrained stiffness matrix.

Arguments:

• acc: element accessor
• acc_immersed: immersed element accessor
• partition: partition
• pullback: bilinear form pullback
• ϕ: level set function
• show_progress: boolean flag for formation progress bar

assemble_boundary(acc::ElementAccessor{Dim}, acc_immersed::ElementAccessor{Dim}, partition::Partition{Dim, T}, pullbacks_boundary::NTuple{N, PullbackBoundary{M}}, ϕ::AlgoimCallLevelSetFunction)

Assemble right hand side vector.

Arguments:

• acc: element accessor
• acc_immersed: immersed element accessor
• partition: partition
• pullbacks_boundary: tuple of 2Dim linear form pullbacks restricted to each boundary
• ϕ: level set function

embedding(width::T, height::T, depth::T)

Return Cartesian background mapping.

embedding(width::T, height::T)

Return Cartesian background mapping.

Taiga.apply_particular_solution(L::LinearOperator, model::ImmersedPotentialFlow, x₀::V)

Return particular solution.

Arguments:

• L: linear operator
• model: model
• x₀: homogeneous solution

Taiga.forcing!(b::AbstractVector, L::LinearOperator, model::ImmersedPotentialFlow)

Update forcing vector.

Arguments:

• b: cache vector
• L: linear operator
• model: model

Taiga.forcing(L::LinearOperator, model::ImmersedPotentialFlow)

Return foring vector.

Taiga.linear_operator(model::ImmersedPotentialFlow; show_progress::Bool = true)

Construct linear operator.