Theory

KitBase.prim_conserveFunction
prim_conserve(prim, γ)

Transform primitive -> conservative variables

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prim_conserve(ρ, U, λ, γ)
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prim_conserve(ρ, U, V, λ, γ)
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prim_conserve(ρ, U, V, W, λ, γ)
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prim_conserve(prim, γ, Kr)

Polyatomic gas

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KitBase.conserve_primFunction
conserve_prim(u)

Transform conservative -> primitive variables

scalar: pseudo primitive vector for scalar conservation laws

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conserve_prim(u, a)
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conserve_prim(W, γ)

vector: primitive vector for Euler, Navier-Stokes and extended equations

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conserve_prim(ρ, M, E, γ)
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conserve_prim(ρ, MX, MY, E, γ)
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conserve_prim(ρ, MX, MY, MZ, E, γ)
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conserve_prim(w, K, Kr)

Rykov model

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KitBase.mixture_prim_conserveFunction
mixture_prim_conserve(prim, γ)

Transform multi-component primitive -> conservative variables

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mixture_prim_conserve(prim, γ, Kr)

Transform multi-component primitive -> conservative variables

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KitBase.mixture_conserve_primFunction
mixture_conserve_prim(W, γ)

Transform multi-component conservative -> primitive variables

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mixture_conserve_prim(W, K, Kr)

Transform multi-component polyatomic conservative -> primitive variables

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Missing docstring.

Missing docstring for em_coefficients. Check Documenter's build log for details.

Missing docstring.

Missing docstring for advection_flux. Check Documenter's build log for details.

Missing docstring.

Missing docstring for burgers_flux. Check Documenter's build log for details.

Missing docstring.

Missing docstring for euler_flux. Check Documenter's build log for details.

Missing docstring.

Missing docstring for euler_jacobi. Check Documenter's build log for details.

Missing docstring.

Missing docstring for gauss_moments. Check Documenter's build log for details.

Missing docstring.

Missing docstring for mixture_gauss_moments. Check Documenter's build log for details.

KitBase.moments_conserveFunction
moments_conserve(Mu, alpha)

Calculate conservative moments of particle distribution

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moments_conserve(Mu, Mxi, alpha, delta)
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moments_conserve(Mu, Mv, Mw, alpha, beta, delta)
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moments_conserve(f, u, ω, _)

Discrete moments of conservative variables

1F1V

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moments_conserve(f, u, v, ω, _)

1F2V

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moments_conserve(h, b, u, ω, _)

2F1V

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moments_conserve(h, b, u, v, ω, _)

2F2V

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moments_conserve(h0, h1, h2, u, v, ω, _)

3F2V

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moments_conserve(f, u, v, w, ω, _)

1F3V

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moments_conserve(h0, h1, h2, h3, u, ω, _)

4F1V

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moments_conserve(f, u, ω)

Shortcut methods

1F1V

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moments_conserve(a1, a2, a3, a4)

2F1V & 1F2V

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moments_conserve(a1, a2, a3, a4, a5)

2F2V & 1F3V

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moments_conserve(a1, a2, a3, a4, a5, a6)

4F1V & 3F2V

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KitBase.mixture_moments_conserveFunction
mixture_moments_conserve(Mu, Mxi, alpha, delta)

Calculate conservative moments of particle distribution in multi-component gas

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mixture_moments_conserve(Mu, Mv, Mw, alpha, beta, delta)
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mixture_moments_conserve(f, u, ω)

Discrete moments of conservative variables

1F1V

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mixture_moments_conserve(h, b, u, ω)

2F1V

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mixture_moments_conserve(h0, h1, h2, h3, u, ω)

4F1V

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mixture_moments_conserve(f, u, v, ω)

1F2V

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mixture_moments_conserve(h, b, u, v, ω)

2F2V

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mixture_moments_conserve(h0, h1, h2, u, v, ω)

3F2V

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mixture_moments_conserve(f, u, v, w, ω)

1F3V

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Missing docstring.

Missing docstring for pdf_slope. Check Documenter's build log for details.

Missing docstring.

Missing docstring for mixture_pdf_slope. Check Documenter's build log for details.

Missing docstring.

Missing docstring for moments_conserve_slope. Check Documenter's build log for details.

Missing docstring.

Missing docstring for mixture_moments_conserve_slope. Check Documenter's build log for details.

KitBase.stressFunction
stress(f, prim, u, ω)

Calculate stress tensor from particle distribution function

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stress(f, prim, u, v, ω)
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stress(f, prim, u, v, w, ω)
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KitBase.heat_fluxFunction
heat_flux(f, prim, u, ω)

Calculate heat flux from particle distribution function

Multiple dispatch doesn't consider unstructured multi-dimensional velocity space. In that case a new method needs to be defined.

1F1V

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heat_flux(h, b, prim, u, ω)

2F1V

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heat_flux(h, b, r, prim, u, ω)

3F1V Rykov model

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heat_flux(h, prim, u, v, ω)

1F2V

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heat_flux(h, b, prim, u, v, ω)

2F2V

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heat_flux(h, b, r, prim, u, v, ω)

3F2V Rykov model

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heat_flux(f, prim, u, v, w, ω)

1F3V

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KitBase.shakhovFunction
shakhov(u, M, q, prim, Pr)

Shakhov non-equilibrium part

1F1V

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shakhov(u, H, B, q, prim, Pr, K)

2F1V

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shakhov(u, v, M, q, prim, Pr)

1F2V

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shakhov(u, v, H, B, q, prim, Pr, K)

2F2V

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shakhov(u, v, w, M, q, prim, Pr)

1F3V

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KitBase.reduce_distributionFunction
reduce_distribution(f, weights)
reduce_distribution(f, weights, dim)

Reduced distribution function

Arguments

  • f: particle distribution function with full velocity space
  • weights: quadrature weights with reduced velocity setting
  • dim: dimension of the reduced distribution function (1 by default)

For 3D -> 1D, the quadrature weights can be obtained from VSpace2D.

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reduce_distribution(f, weights)
reduce_distribution(f, weights, dim)
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reduce_distribution(f, v, w, weights)
reduce_distribution(f, v, w, weights, dim)
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KitBase.full_distributionFunction
full_distribution(h, b, u, weights, v, w, ρ)
full_distribution(h, b, u, weights, v, w, ρ, γ)

Recover full distribution function from reduced ones

Arguments

  • h, b: reduced particle distribution function with 1D velocity space
  • u: quadrature nodes in 1D velocity space
  • weights: quadrature weights in 1D velocity space
  • v, w: quadrature nodes in the rest velocity space (with 3D setting)

Outputs

  • f: particle distribution function with 3D velocity space
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full_distribution(h, b, u, weights, v, w, prim)
full_distribution(h, b, u, weights, v, w, prim, γ)
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KitBase.ref_vhs_visFunction
ref_vhs_vis(Kn, alpha, omega)

Calculate reference viscosity with variable hard sphere (VHS) model

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KitBase.vhs_collision_timeFunction
vhs_collision_time(ρ, λ, μᵣ, ω)

Calculate collision time with variable hard sphere (VHS) model

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vhs_collision_time(prim, muRef, omega)

For Rykov model prim[end] should be λₜ

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KitBase.aap_hs_primFunction
aap_hs_prim(prim, tau, mi, ni, me, ne, kn)

Calculate mixture primitive variables from AAP model

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Missing docstring.

Missing docstring for aap_hs_diffeq!. Check Documenter's build log for details.

KitBase.shift_pdf!Function
shift_pdf!(f, a, du, dt)

Shift distribution function by external force

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shift_pdf!(f, a, du, dt)

Multi-component gas

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KitBase.hs_boltz_knFunction
hs_boltz_kn(mu_ref, alpha)

Calculate effective Knudsen number for fast spectral method with hard sphere (HS) model

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KitBase.kernel_modeFunction
kernel_mode(
    M::Integer,
    umax,
    vmax,
    wmax,
    du,
    dv,
    dw,
    unum::Integer,
    vnum::Integer,
    wnum::Integer,
    alpha;
    quad_num
) -> Tuple{Any, Any, Array{Float64, 3}}

Calculate collision kernel for fast spectral method...

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kernel_mode(
    M::Integer,
    umax,
    vmax,
    wmax,
    unum::Integer,
    vnum::Integer,
    wnum::Integer,
    alpha;
    quad_num
) -> Tuple{Any, Any, Array{Float64, 3}}
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kernel_mode(
    M::Integer,
    umax,
    vmax,
    du,
    dv,
    unum::Integer,
    vnum::Integer;
    quad_num
) -> Tuple{Array{Float64, 3}, Array{Float64, 3}, Matrix{Float64}}
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KitBase.boltzmann_fftFunction
boltzmann_fft(
    f0::AbstractArray{<:Real, 3},
    Kn,
    M::Integer,
    ϕ::AbstractArray{<:Real, 4},
    ψ::AbstractArray{<:Real, 4},
    phipsi::AbstractArray{<:Real, 3}
) -> Any

Calculate collision operator with FFT-based fast spectral method...

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boltzmann_fft(f, p)
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KitBase.boltzmann_fft!Function
boltzmann_fft!(
    Q::AbstractArray{<:Real, 3},
    f0::AbstractArray{<:Real, 3},
    Kn::Real,
    M::Integer,
    ϕ::AbstractArray{<:Real, 4},
    ψ::AbstractArray{<:Real, 4},
    phipsi::AbstractArray{<:Real, 3}
) -> Any

Calculate collision operator with FFT-based fast spectral method...

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boltzmann_fft!(Q, f, p)
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KitBase.heat_capacity_ratioFunction
heat_capacity_ratio(K, D)

Calculate heat capacity ratio (monatomic gas)

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heat_capacity_ratio(K, Nr, D)

Calculate heat capacity ratio (diatomic gas)

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