/
flux_kcu.jl
1189 lines (993 loc) · 27.4 KB
/
flux_kcu.jl
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"""
$(SIGNATURES)
Kinetic central-upwind (KCU) flux
"""
flux_kcu!(KS::AbstractSolverSet, face, ctrL, ctrR, args...) =
flux_kcu!(face, ctrL, ctrR, KS.gas, KS.vs, args...)
"""
$(SIGNATURES)
"""
function flux_kcu!(
face::Interface1F,
ctrL::T,
ctrR::T,
gas::AbstractProperty,
vs::AbstractVelocitySpace1D,
p,
dt = 1.0,
) where {T<:ControlVolume1F}
dxL, dxR = p[1:2]
flux_kcu!(
face.fw,
face.ff,
ctrL.w + ctrL.sw * dxL,
ctrL.f + ctrL.sf * dxL,
ctrR.w - ctrR.sw * dxR,
ctrR.f - ctrR.sf * dxR,
vs.u,
vs.weights,
gas.K,
gas.γ,
gas.μᵣ,
gas.ω,
gas.Pr,
dt,
)
return nothing
end
"""
$(SIGNATURES)
"""
function flux_kcu!(
face::Interface2F,
ctrL::T,
ctrR::T,
gas::AbstractProperty,
vs::AbstractVelocitySpace1D,
p,
dt = 1.0,
) where {T<:ControlVolume2F}
dxL, dxR = p[1:2]
if gas isa Mixture
flux_kcu!(
face.fw,
face.fh,
face.fb,
ctrL.w + ctrL.sw * dxL,
ctrL.h + ctrL.sh * dxL,
ctrL.b + ctrL.sb * dxL,
ctrR.w - ctrR.sw * dxR,
ctrR.h - ctrR.sh * dxR,
ctrR.b - ctrR.sb * dxR,
vs.u,
vs.weights,
gas.K,
gas.γ,
gas.mi,
gas.ni,
gas.me,
gas.ne,
gas.Kn[1],
dt,
)
else
flux_kcu!(
face.fw,
face.fh,
face.fb,
ctrL.w + ctrL.sw * dxL,
ctrL.h + ctrL.sh * dxL,
ctrL.b + ctrL.sb * dxL,
ctrR.w - ctrR.sw * dxR,
ctrR.h - ctrR.sh * dxR,
ctrR.b - ctrR.sb * dxR,
vs.u,
vs.weights,
gas.K,
gas.γ,
gas.μᵣ,
gas.ω,
gas.Pr,
dt,
)
end
return nothing
end
"""
$(SIGNATURES)
"""
function flux_kcu!(
face::Interface1F,
ctrL::T,
ctrR::T,
gas::AbstractProperty,
vs::AbstractVelocitySpace2D,
p,
dt = 1.0,
) where {T<:ControlVolume1F}
dxL, dxR, len, n, dirc = p
swL = extract_last(ctrL.sw, dirc; mode = :view)
swR = extract_last(ctrR.sw, dirc; mode = :view)
sfL = extract_last(ctrL.sf, dirc; mode = :view)
sfR = extract_last(ctrR.sf, dirc; mode = :view)
flux_kcu!(
face.fw,
face.ff,
local_frame(ctrL.w .+ dxL .* swL, n),
ctrL.f .+ dxL .* sfL,
local_frame(ctrR.w .- dxR .* swR, n),
ctrR.f .- dxR .* sfR,
vs.u .* n[1] .+ vs.v .* n[2],
vs.v .* n[1] .- vs.u .* n[2],
vs.weights,
gas.K,
gas.γ,
gas.μᵣ,
gas.ω,
gas.Pr,
dt,
len,
)
face.fw .= global_frame(face.fw, n)
return nothing
end
"""
$(SIGNATURES)
"""
function flux_kcu!(
face::Interface2F,
ctrL::T,
ctrR::T,
gas::AbstractProperty,
vs::AbstractVelocitySpace2D,
p,
dt = 1.0,
) where {T<:ControlVolume2F}
dxL, dxR, len, n, dirc = p
swL = extract_last(ctrL.sw, dirc; mode = :view)
swR = extract_last(ctrR.sw, dirc; mode = :view)
shL = extract_last(ctrL.sh, dirc; mode = :view)
sbL = extract_last(ctrL.sb, dirc; mode = :view)
shR = extract_last(ctrR.sh, dirc; mode = :view)
sbR = extract_last(ctrR.sb, dirc; mode = :view)
flux_kcu!(
face.fw,
face.fh,
face.fb,
local_frame(ctrL.w .+ dxL .* swL, n),
ctrL.h .+ dxL .* shL,
ctrL.b .+ dxL .* sbL,
local_frame(ctrR.w .- dxR .* swR, n),
ctrR.h .- dxR .* shR,
ctrR.b .- dxR .* sbR,
vs.u .* n[1] .+ vs.v .* n[2],
vs.v .* n[1] .- vs.u .* n[2],
vs.weights,
gas.K,
gas.γ,
gas.μᵣ,
gas.ω,
gas.Pr,
dt,
len,
)
face.fw .= global_frame(face.fw, n)
return nothing
end
"""
$(SIGNATURES)
"""
function flux_kcu!(
face::Interface1F,
ctrL::T,
ctrR::T,
gas::AbstractProperty,
vs::AbstractVelocitySpace3D,
p,
dt = 1.0,
) where {T<:ControlVolume1F}
dxL, dxR = p[1:2]
if length(p) == 2 || p[3] == 1
flux_kcu!(
face.fw,
face.ff,
ctrL.w .+ dxL .* ctrL.sw,
ctrL.f .+ dxL .* ctrL.sf,
ctrR.w .- dxR .* ctrR.sw,
ctrR.f .- dxR .* ctrR.sf,
vs.u,
vs.v,
vs.w,
vs.weights,
gas.K,
gas.γ,
gas.μᵣ,
gas.ω,
gas.Pr,
dt,
)
else
end
return nothing
end
# ------------------------------------------------------------
# Low-level backends
# ------------------------------------------------------------
"""
$(SIGNATURES)
1D1F1V
"""
function flux_kcu!(
fw::X,
ff::Y,
wL::Z,
fL::A,
wR::Z,
fR::A,
u::B,
ω::B,
inK,
γ,
visRef,
visIdx,
Pr,
dt,
) where {X<:AA{<:FN,1},Y<:AA{<:FN,1},Z<:AA{<:Real,1},A<:AA{<:FN,1},B<:AA{<:FN,1}} # 1D1F1V
# upwind reconstruction
δ = heaviside.(u)
f = @. fL * δ + fR * (1.0 - δ)
primL = conserve_prim(wL, γ)
primR = conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mxi1, MuL1, MuR1 = gauss_moments(primL, inK)
Muv1 = moments_conserve(MuL1, Mxi1, 0, 0)
Mu2, Mxi2, MuL2, MuR2 = gauss_moments(primR, inK)
Muv2 = moments_conserve(MuR2, Mxi2, 0, 0)
w = similar(wL)
@. w = primL[1] * Muv1 + primR[1] * Muv2
prim = conserve_prim(w, γ)
tau = vhs_collision_time(prim, visRef, visIdx)
tau +=
abs(primL[1] / primL[end] - primR[1] / primR[end]) /
(primL[1] / primL[end] + primR[1] / primR[end]) *
dt *
2.0
Mt = zeros(2)
Mt[2] = tau * (1.0 - exp(-dt / tau)) # f0
Mt[1] = dt - Mt[2] # M0
# calculate fluxes
Mu, Mxi, MuL, MuR = gauss_moments(prim, inK)
## flux from M0
Muv = moments_conserve(Mu, Mxi, 1, 0)
@. fw = Mt[1] * prim[1] * Muv
## flux from f0
g = maxwellian(u, prim)
fw[1] += Mt[2] * sum(ω .* u .* f)
fw[2] += Mt[2] * sum(ω .* u .^ 2 .* f)
fw[3] += Mt[2] * 0.5 * (sum(ω .* u .^ 3 .* f))
@. ff = Mt[1] * u * g + Mt[2] * u * f
return nothing
end
"""
$(SIGNATURES)
Mixture
"""
function flux_kcu!(
fw::X,
ff::Y,
wL::Z,
fL::A,
wR::Z,
fR::A,
u::B,
ω::B,
inK,
γ,
mi,
ni,
me,
ne,
Kn,
dt,
) where {X<:AA{<:FN,2},Y<:AA{<:FN,2},Z<:AA{<:Real,2},A<:AA{<:FN,2},B<:AA{<:FN,2}}
# upwind reconstruction
δ = heaviside.(u)
f = @. fL * δ + fR * (1.0 - δ)
primL = mixture_conserve_prim(wL, γ)
primR = mixture_conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mxi1, MuL1, MuR1 = mixture_gauss_moments(primL, inK)
Mu2, Mxi2, MuL2, MuR2 = mixture_gauss_moments(primR, inK)
Muv1 = mixture_moments_conserve(MuL1, Mxi1, 0, 0)
Muv2 = mixture_moments_conserve(MuR2, Mxi2, 0, 0)
w = similar(wL)
for j in axes(w, 2)
@. w[:, j] = primL[1, j] * Muv1[:, j] + primR[1, j] * Muv2[:, j]
end
prim = mixture_conserve_prim(w, γ)
tau = aap_hs_collision_time(prim, mi, ni, me, ne, Kn)
#@. tau +=
# abs(cellL.prim[1, :] / cellL.prim[end, :] - cellR.prim[1, :] / cellR.prim[end, :]) /
# (cellL.prim[1, :] / cellL.prim[end, :] + cellR.prim[1, :] / cellR.prim[end, :]) *
# dt *
# 2.0
prim = aap_hs_prim(prim, tau, mi, ni, me, ne, Kn)
Mt = zeros(2, 2)
@. Mt[2, :] = tau * (1.0 - exp(-dt / tau)) # f0
@. Mt[1, :] = dt - Mt[2, :] # M0
# calculate fluxes
Mu, Mxi, MuL, MuR = mixture_gauss_moments(prim, inK)
Muv = mixture_moments_conserve(Mu, Mxi, 1, 0)
## flux from M0
for j in axes(fw, 2)
@. fw[:, j] = Mt[1, j] * prim[1, j] * Muv[:, j]
end
## flux from f0
M = mixture_maxwellian(u, prim)
for j in axes(fw, 2)
fw[1, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .* f[:, j])
fw[2, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .^ 2 .* f[:, j])
fw[3, j] += Mt[2, j] * 0.5 * sum(ω[:, j] .* u[:, j] .^ 3 .* f[:, j])
@. ff[:, j] = Mt[1, j] * u[:, j] * M[:, j] + Mt[2, j] * u[:, j] * f[:, j]
end
return nothing
end
"""
$(SIGNATURES)
1D1F3V
"""
function flux_kcu!(
fw::X,
ff::Y,
wL::Z,
fL::A,
wR::Z,
fR::A,
uVelo::B,
vVelo::B,
wVelo::B,
ω::B,
inK,
γ,
visRef,
visIdx,
Pr,
dt,
len = 1.0,
) where {X<:AA{<:FN,1},Y<:AA{<:FN,3},Z<:AA{<:Real,1},A<:AA{<:FN,3},B<:AA{<:FN,3}} # 1D1F1V
# upwind reconstruction
δ = heaviside.(uVelo)
f = @. fL * δ + fR * (1.0 - δ)
primL = conserve_prim(wL, γ)
primR = conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mv1, Mw1, MuL1, MuR1 = gauss_moments(primL, inK)
Muv1 = moments_conserve(MuL1, Mv1, Mw1, 0, 0, 0)
Mu2, Mv2, Mw2, MuL2, MuR2 = gauss_moments(primR, inK)
Muv2 = moments_conserve(MuR2, Mv2, Mw2, 0, 0, 0)
w = similar(wL)
@. w = primL[1] * Muv1 + primR[1] * Muv2
prim = conserve_prim(w, γ)
tau = vhs_collision_time(prim, visRef, visIdx)
tau +=
abs(primL[1] / primL[end] - primR[1] / primR[end]) /
(primL[1] / primL[end] + primR[1] / primR[end]) *
dt *
2.0
Mt = zeros(2)
Mt[2] = tau * (1.0 - exp(-dt / tau)) # f0
Mt[1] = dt - Mt[2] # M0
# calculate fluxes
Mu, Mv, Mw, MuL, MuR = gauss_moments(prim, inK)
## flux from M0
Muv = moments_conserve(Mu, Mv, Mw, 1, 0, 0)
@. fw = Mt[1] * prim[1] * Muv
## flux from f0
g = maxwellian(uVelo, vVelo, wVelo, prim)
fw[1] += Mt[2] * sum(ω .* uVelo .* f)
fw[2] += Mt[2] * sum(ω .* uVelo .^ 2 .* f)
fw[3] += Mt[2] * sum(ω .* uVelo .* vVelo .* f)
fw[4] += Mt[2] * sum(ω .* uVelo .* wVelo .* f)
fw[5] += Mt[2] * 0.5 * sum(ω .* uVelo .* (uVelo .^ 2 .+ vVelo .^ 2 .+ wVelo .^ 2) .* f)
@. fw .*= len
@. ff = (Mt[1] * uVelo * g + Mt[2] * uVelo * f) * len
return nothing
end
"""
$(SIGNATURES)
1D2F1V
"""
function flux_kcu!(
fw::X,
fh::Y,
fb::Y,
wL::Z,
hL::A,
bL::A,
wR::Z,
hR::A,
bR::A,
u::B,
ω::B,
inK,
γ,
visRef,
visIdx,
Pr,
dt,
) where {X<:AA{<:FN,1},Y<:AA{<:FN,1},Z<:AA{<:Real,1},A<:AA{<:FN,1},B<:AA{<:FN,1}}
# upwind reconstruction
δ = heaviside.(u)
h = @. hL * δ + hR * (1.0 - δ)
b = @. bL * δ + bR * (1.0 - δ)
primL = conserve_prim(wL, γ)
primR = conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mxi1, MuL1, MuR1 = gauss_moments(primL, inK)
Muv1 = moments_conserve(MuL1, Mxi1, 0, 0)
Mu2, Mxi2, MuL2, MuR2 = gauss_moments(primR, inK)
Muv2 = moments_conserve(MuR2, Mxi2, 0, 0)
w = @. primL[1] * Muv1 + primR[1] * Muv2
prim = conserve_prim(w, γ)
tau = vhs_collision_time(prim, visRef, visIdx)
tau +=
abs(primL[1] / primL[end] - primR[1] / primR[end]) /
(primL[1] / primL[end] + primR[1] / primR[end]) *
dt *
2.0
Mt = zeros(2)
Mt[2] = tau * (1.0 - exp(-dt / tau)) # f0
Mt[1] = dt - Mt[2] # M0
# calculate fluxes
Mu, Mxi, MuL, MuR = gauss_moments(prim, inK)
## flux from M0
Muv = moments_conserve(Mu, Mxi, 1, 0)
@. fw = Mt[1] * prim[1] * Muv
## flux from f0
Mh = maxwellian(u, prim)
Mb = Mh .* inK ./ (2.0 * prim[end])
fw[1] += Mt[2] * sum(ω .* u .* h)
fw[2] += Mt[2] * sum(ω .* u .^ 2 .* h)
fw[3] += Mt[2] * 0.5 * (sum(ω .* u .^ 3 .* h) + sum(ω .* u .* b))
@. fh = Mt[1] * u * Mh + Mt[2] * u * h
@. fb = Mt[1] * u * Mb + Mt[2] * u * b
return nothing
end
"""
$(SIGNATURES)
Mixture
"""
function flux_kcu!(
fw::T1,
fh::T2,
fb::T2,
wL::T3,
hL::T4,
bL::T4,
wR::T3,
hR::T4,
bR::T4,
u::T5,
ω::T5,
inK,
γ,
mi,
ni,
me,
ne,
Kn,
dt,
) where {T1<:AA{<:FN,2},T2<:AA{<:FN,2},T3<:AA{<:Real,2},T4<:AA{<:FN,2},T5<:AA{<:FN,2}}
# upwind reconstruction
δ = heaviside.(u)
h = @. hL * δ + hR * (1.0 - δ)
b = @. bL * δ + bR * (1.0 - δ)
primL = mixture_conserve_prim(wL, γ)
primR = mixture_conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mxi1, MuL1, MuR1 = mixture_gauss_moments(primL, inK)
Mu2, Mxi2, MuL2, MuR2 = mixture_gauss_moments(primR, inK)
Muv1 = mixture_moments_conserve(MuL1, Mxi1, 0, 0)
Muv2 = mixture_moments_conserve(MuR2, Mxi2, 0, 0)
w = similar(wL)
for j in axes(w, 2)
@. w[:, j] = primL[1, j] * Muv1[:, j] + primR[1, j] * Muv2[:, j]
end
prim = mixture_conserve_prim(w, γ)
tau = aap_hs_collision_time(prim, mi, ni, me, ne, Kn)
#@. tau +=
# abs(cellL.prim[1, :] / cellL.prim[end, :] - cellR.prim[1, :] / cellR.prim[end, :]) /
# (cellL.prim[1, :] / cellL.prim[end, :] + cellR.prim[1, :] / cellR.prim[end, :]) *
# dt *
# 2.0
prim = aap_hs_prim(prim, tau, mi, ni, me, ne, Kn)
Mt = zeros(2, 2)
@. Mt[2, :] = tau * (1.0 - exp(-dt / tau)) # f0
@. Mt[1, :] = dt - Mt[2, :] # M0
# calculate fluxes
Mu, Mxi, MuL, MuR = mixture_gauss_moments(prim, inK)
Muv = mixture_moments_conserve(Mu, Mxi, 1, 0)
## flux from M0
for j in axes(fw, 2)
@. fw[:, j] = Mt[1, j] * prim[1, j] * Muv[:, j]
end
## flux from f0
MH = mixture_maxwellian(u, prim)
MB = similar(MH)
for j in axes(MB, 2)
MB[:, j] .= MH[:, j] .* inK ./ (2.0 * prim[end, j])
end
for j in axes(fw, 2)
fw[1, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .* h[:, j])
fw[2, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .^ 2 .* h[:, j])
fw[3, j] +=
Mt[2, j] *
0.5 *
(sum(ω[:, j] .* u[:, j] .^ 3 .* h[:, j]) + sum(ω[:, j] .* u[:, j] .* b[:, j]))
@. fh[:, j] = Mt[1, j] * u[:, j] * MH[:, j] + Mt[2, j] * u[:, j] * h[:, j]
@. fb[:, j] = Mt[1, j] * u[:, j] * MB[:, j] + Mt[2, j] * u[:, j] * b[:, j]
end
return nothing
end
"""
$(SIGNATURES)
1D4F1V
"""
function flux_kcu!(
fw::X,
fh0::Y,
fh1::Y,
fh2::Y,
fh3::Y,
wL::Z,
h0L::A,
h1L::A,
h2L::A,
h3L::A,
wR::Z,
h0R::A,
h1R::A,
h2R::A,
h3R::A,
u::B,
ω::B,
inK,
γ,
visRef,
visIdx,
Pr,
dt,
) where {X<:AA{<:FN,1},Y<:AA{<:FN,1},Z<:AA{<:Real,1},A<:AA{<:FN,1},B<:AA{<:FN,1}}
# upwind reconstruction
δ = heaviside.(u)
h0 = @. h0L * δ + h0R * (1.0 - δ)
h1 = @. h1L * δ + h1R * (1.0 - δ)
h2 = @. h2L * δ + h2R * (1.0 - δ)
h3 = @. h3L * δ + h3R * (1.0 - δ)
primL = conserve_prim(wL, γ)
primR = conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mv1, Mw1, MuL1, MuR1 = gauss_moments(primL, inK)
Muv1 = moments_conserve(MuL1, Mv1, Mw1, 0, 0, 0)
Mu2, Mv2, Mw2, MuL2, MuR2 = gauss_moments(primR, inK)
Muv2 = moments_conserve(MuR2, Mv2, Mw2, 0, 0, 0)
w = @. primL[1] * Muv1 + primR[1] * Muv2
prim = conserve_prim(w, γ)
tau = vhs_collision_time(prim, visRef, visIdx)
tau +=
abs(primL[1] / primL[end] - primR[1] / primR[end]) /
(primL[1] / primL[end] + primR[1] / primR[end]) *
dt *
2.0
Mt = zeros(2)
Mt[2] = tau * (1.0 - exp(-dt / tau)) # f0
Mt[1] = dt - Mt[2] # M0
# calculate fluxes
Mu, Mv, Mw, MuL, MuR = gauss_moments(prim, inK)
## flux from M0
Muv = moments_conserve(Mu, Mv, Mw, 1, 0, 0)
@. fw = Mt[1] * prim[1] * Muv
## flux from f0
g0 = maxwellian(u, prim)
g1 = Mv[1] .* g0
g2 = Mw[1] .* g0
g3 = (Mv[2] + Mw[2]) .* g0
fw[1] += Mt[2] * sum(ω .* u .* h0)
fw[2] += Mt[2] * sum(ω .* u .^ 2 .* h0)
fw[3] += Mt[2] * sum(ω .* u .* h1)
fw[4] += Mt[2] * sum(ω .* u .* h2)
fw[5] += Mt[2] * 0.5 * (sum(ω .* u .^ 3 .* h0) + sum(ω .* u .* h3))
@. fh0 = Mt[1] * u * g0 + Mt[2] * u * h0
@. fh1 = Mt[1] * u * g1 + Mt[2] * u * h1
@. fh2 = Mt[1] * u * g2 + Mt[2] * u * h2
@. fh3 = Mt[1] * u * g3 + Mt[2] * u * h3
return nothing
end
"""
$(SIGNATURES)
Mixture
"""
function flux_kcu!(
fw::X,
fh0::Y,
fh1::Y,
fh2::Y,
fh3::Y,
wL::Z,
h0L::A,
h1L::A,
h2L::A,
h3L::A,
wR::Z,
h0R::A,
h1R::A,
h2R::A,
h3R::A,
u::B,
ω::B,
inK,
γ,
mi,
ni,
me,
ne,
Kn,
dt,
isMHD = false::Bool,
) where {X<:AA{<:FN,2},Y<:AA{<:FN,2},Z<:AA{<:Real,2},A<:AA{<:FN,2},B<:AA{<:FN,2}}
#--- upwind reconstruction ---#
δ = heaviside.(u)
h0 = @. h0L * δ + h0R * (1.0 - δ)
h1 = @. h1L * δ + h1R * (1.0 - δ)
h2 = @. h2L * δ + h2R * (1.0 - δ)
h3 = @. h3L * δ + h3R * (1.0 - δ)
primL = mixture_conserve_prim(wL, γ)
primR = mixture_conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mv1, Mw1, MuL1, MuR1 = mixture_gauss_moments(primL, inK)
Muv1 = mixture_moments_conserve(MuL1, Mv1, Mw1, 0, 0, 0)
Mu2, Mv2, Mw2, MuL2, MuR2 = mixture_gauss_moments(primR, inK)
Muv2 = mixture_moments_conserve(MuR2, Mv2, Mw2, 0, 0, 0)
w = similar(wL)
for j in axes(w, 2)
@. w[:, j] = primL[1, j] * Muv1[:, j] + primR[1, j] * Muv2[:, j]
end
prim = mixture_conserve_prim(w, γ)
tau = aap_hs_collision_time(prim, mi, ni, me, ne, Kn)
#@. tau +=
# abs(primL[1, :] / primL[end, :] - primR[1, :] / primR[end, :]) /
# (primL[1, :] / primL[end, :] + primR[1, :] / primR[end, :]) *
# dt *
# 5.0
if !isMHD
prim = aap_hs_prim(prim, tau, mi, ni, me, ne, Kn)
end
Mt = zeros(2, 2)
@. Mt[2, :] = tau * (1.0 - exp(-dt / tau)) # f0
@. Mt[1, :] = dt - Mt[2, :] # M0
# calculate fluxes
Mu, Mv, Mw, MuL, MuR = mixture_gauss_moments(prim, inK)
Muv = mixture_moments_conserve(Mu, Mv, Mw, 1, 0, 0)
## flux from M0
for j in axes(fw, 2)
@. fw[:, j] = Mt[1, j] * prim[1, j] * Muv[:, j]
end
## flux from f0
g0 = mixture_maxwellian(u, prim)
g1 = similar(h0)
g2 = similar(h0)
g3 = similar(h0)
for j in axes(g0, 2)
g1[:, j] .= Mv[1, j] .* g0[:, j]
g2[:, j] .= Mw[1, j] .* g0[:, j]
g3[:, j] .= (Mv[2, j] + Mw[2, j]) .* g0[:, j]
end
for j in axes(fw, 2)
fw[1, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .* h0[:, j])
fw[2, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .^ 2 .* h0[:, j])
fw[3, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .* h1[:, j])
fw[4, j] += Mt[2, j] * sum(ω[:, j] .* u[:, j] .* h2[:, j])
fw[5, j] +=
Mt[2, j] *
0.5 *
(sum(ω[:, j] .* u[:, j] .^ 3 .* h0[:, j]) + sum(ω[:, j] .* u[:, j] .* h3[:, j]))
@. fh0[:, j] = Mt[1, j] * u[:, j] * g0[:, j] + Mt[2, j] * u[:, j] * h0[:, j]
@. fh1[:, j] = Mt[1, j] * u[:, j] * g1[:, j] + Mt[2, j] * u[:, j] * h1[:, j]
@. fh2[:, j] = Mt[1, j] * u[:, j] * g2[:, j] + Mt[2, j] * u[:, j] * h2[:, j]
@. fh3[:, j] = Mt[1, j] * u[:, j] * g3[:, j] + Mt[2, j] * u[:, j] * h3[:, j]
end
return nothing
end
"""
$(SIGNATURES)
2D1F2V
"""
function flux_kcu!(
fw::X,
ff::Y,
wL::Z,
fL::A,
wR::Z,
fR::A,
u::B,
v::B,
ω::B,
inK,
γ,
visRef,
visIdx,
Pr,
dt,
len,
) where {X<:AA{<:FN,1},Y<:AA{<:FN,2},Z<:AA{<:Real,1},A<:AA{<:FN,2},B<:AA{<:FN,2}}
# reconstruct initial distribution
δ = heaviside.(u)
f = @. fL * δ + fR * (1.0 - δ)
primL = conserve_prim(wL, γ)
primR = conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mv1, Mxi1, MuL1, MuR1 = gauss_moments(primL, inK)
Muv1 = moments_conserve(MuL1, Mv1, Mxi1, 0, 0, 0)
Mu2, Mv2, Mxi2, MuL2, MuR2 = gauss_moments(primR, inK)
Muv2 = moments_conserve(MuR2, Mv2, Mxi2, 0, 0, 0)
w = @. primL[1] * Muv1 + primR[1] * Muv2
prim = conserve_prim(w, γ)
tau = vhs_collision_time(prim, visRef, visIdx)
tau +=
abs(primL[1] / primL[end] - primR[1] / primR[end]) /
(primL[1] / primL[end] + primR[1] / primR[end]) *
dt *
2.0
Mt = zeros(2)
Mt[2] = tau * (1.0 - exp(-dt / tau)) # f0
Mt[1] = dt - Mt[2] # M0
# calculate interface flux
Mu, Mv, Mxi, MuL, MuR = gauss_moments(prim, inK)
## flux from M0
Muv = moments_conserve(Mu, Mv, Mxi, 1, 0, 0)
@. fw = Mt[1] * prim[1] * Muv * len
## flux from f0
g = maxwellian(u, v, prim)
fw[1] += Mt[2] * sum(ω .* u .* f) * len
fw[2] += Mt[2] * sum(ω .* u .^ 2 .* f) * len
fw[3] += Mt[2] * sum(ω .* v .* u .* f) * len
fw[4] += Mt[2] * 0.5 * (sum(ω .* u .* (u .^ 2 .+ v .^ 2) .* f)) * len
@. ff = (Mt[1] * u * g + Mt[2] * u * f) * len
return nothing
end
"""
$(SIGNATURES)
2D2F2V
"""
function flux_kcu!(
fw::T1,
fh::T2,
fb::T2,
wL::T3,
hL::T4,
bL::T4,
wR::T3,
hR::T4,
bR::T4,
u::T5,
v::T5,
ω::T5,
inK,
γ,
visRef,
visIdx,
Pr,
dt,
len,
) where {T1<:AA{<:FN,1},T2<:AA{<:FN,2},T3<:AA{<:Real,1},T4<:AA{<:FN,2},T5<:AA{<:FN,2}}
# reconstruct initial distribution
δ = heaviside.(u)
h = @. hL * δ + hR * (1.0 - δ)
b = @. bL * δ + bR * (1.0 - δ)
primL = conserve_prim(wL, γ)
primR = conserve_prim(wR, γ)
# construct interface distribution
Mu1, Mv1, Mxi1, MuL1, MuR1 = gauss_moments(primL, inK)
Muv1 = moments_conserve(MuL1, Mv1, Mxi1, 0, 0, 0)
Mu2, Mv2, Mxi2, MuL2, MuR2 = gauss_moments(primR, inK)
Muv2 = moments_conserve(MuR2, Mv2, Mxi2, 0, 0, 0)
w = @. primL[1] * Muv1 + primR[1] * Muv2
prim = conserve_prim(w, γ)
tau = vhs_collision_time(prim, visRef, visIdx)
tau +=
abs(primL[1] / primL[end] - primR[1] / primR[end]) /
(primL[1] / primL[end] + primR[1] / primR[end]) *
dt *
2.0
Mt = zeros(2)
Mt[2] = tau * (1.0 - exp(-dt / tau)) # f0
Mt[1] = dt - Mt[2] # M0
# calculate interface flux
Mu, Mv, Mxi, MuL, MuR = gauss_moments(prim, inK)
## flux from M0
Muv = moments_conserve(Mu, Mv, Mxi, 1, 0, 0)
@. fw = Mt[1] * prim[1] * Muv * len
## flux from f0
H = maxwellian(u, v, prim)
B = H .* inK ./ (2.0 * prim[end])
fw[1] += Mt[2] * sum(ω .* u .* h) * len
fw[2] += Mt[2] * sum(ω .* u .^ 2 .* h) * len
fw[3] += Mt[2] * sum(ω .* v .* u .* h) * len
fw[4] += Mt[2] * 0.5 * (sum(ω .* u .* (u .^ 2 .+ v .^ 2) .* h) + sum(ω .* u .* b)) * len
@. fh = (Mt[1] * u * H + Mt[2] * u * h) * len
@. fb = (Mt[1] * u * B + Mt[2] * u * b) * len
return nothing
end
"""
$(SIGNATURES)
2D3F2V
"""
function flux_kcu!(
fw::X,
fh0::Y,
fh1::Y,
fh2::Y,
wL::Z,
h0L::A,