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schemes.jl
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schemes.jl
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function shockSensor(ϕ, Q)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i < 2 || i > Nxp+2*NG-1 || j < 2 || j > Ny+2*NG-1 || k < 2 || k > Nz+2*NG-1
return
end
@inbounds Px1 = Q[i-1, j, k, 5]
@inbounds Px2 = Q[i, j, k, 5]
@inbounds Px3 = Q[i+1, j, k, 5]
@inbounds Py1 = Q[i, j-1, k, 5]
@inbounds Py2 = Q[i, j, k, 5]
@inbounds Py3 = Q[i, j+1, k, 5]
@inbounds Pz1 = Q[i, j, k-1, 5]
@inbounds Pz2 = Q[i, j, k , 5]
@inbounds Pz3 = Q[i, j, k+1, 5]
ϕx = abs(-Px1 + 2*Px2 - Px3)/(Px1 + 2*Px2 + Px3)
ϕy = abs(-Py1 + 2*Py2 - Py3)/(Py1 + 2*Py2 + Py3)
ϕz = abs(-Pz1 + 2*Pz2 - Pz3)/(Pz1 + 2*Pz2 + Pz3)
@inbounds ϕ[i, j, k] = ϕx + ϕy + ϕz
return
end
@inline function minmod(a, b)
ifelse(a*b > 0, (abs(a) > abs(b)) ? b : a, zero(a))
end
#Range: 1 -> N+1
function NND_x(F, Fp, Fm, NV)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG+1 || j > Ny+NG || k > Nz+NG || i < 1+NG || j < 1+NG || k < 1+NG
return
end
for n = 1:NV
@inbounds fp = Fp[i-1, j, k, n] + 0.5*minmod(Fp[i, j, k, n] - Fp[i-1, j, k, n],
Fp[i-1, j, k, n] - Fp[i-2, j, k, n])
@inbounds fm = Fm[i, j, k, n] - 0.5*minmod(Fm[i+1, j, k, n] - Fm[i, j, k, n],
Fm[i, j, k, n] - Fm[i-1, j, k, n])
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
return
end
function NND_y(F, Fp, Fm, NV)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG || j > Ny+NG+1 || k > Nz+NG || i < 1+NG || j < 1+NG || k < 1+NG
return
end
for n = 1:NV
@inbounds fp = Fp[i, j-1, k, n] + 0.5*minmod(Fp[i, j, k, n] - Fp[i, j-1, k, n],
Fp[i, j-1, k, n] - Fp[i, j-2, k, n])
@inbounds fm = Fm[i, j, k, n] - 0.5*minmod(Fm[i, j+1, k, n] - Fm[i, j, k, n],
Fm[i, j, k, n] - Fm[i, j-1, k, n])
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
return
end
function NND_z(F, Fp, Fm, NV)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG || j > Ny+NG || k > Nz+NG+1 || i < 1+NG || j < 1+NG || k < 1+NG
return
end
for n = 1:NV
@inbounds fp = Fp[i, j, k-1, n] + 0.5*minmod(Fp[i, j, k, n] - Fp[i, j, k-1, n],
Fp[i, j, k-1, n] - Fp[i, j, k-2, n])
@inbounds fm = Fm[i, j, k, n] - 0.5*minmod(Fm[i, j, k+1, n] - Fm[i, j, k, n],
Fm[i, j, k, n] - Fm[i, j, k-1, n])
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
return
end
#Range: 1 -> N+1
function WENO_x(F, ϕ, Fp, Fm, NV, tag)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG+1 || j > Ny+NG || k > Nz+NG || i < 1+NG || j < 1+NG || k < 1+NG
return
end
if tag[i, j, k] == 1
return
end
tmp1::Float64 = 13/12
tmp2::Float64 = 1/6
c1::Float64 = UP7[1]
c2::Float64 = UP7[2]
c3::Float64 = UP7[3]
c4::Float64 = UP7[4]
c5::Float64 = UP7[5]
c6::Float64 = UP7[6]
c7::Float64 = UP7[7]
# Jameson sensor
@inbounds ϕx = max(ϕ[i-1, j, k], ϕ[i, j, k])
if ϕx < hybrid_ϕ1
for n = 1:NV
@inbounds V1 = Fp[i-4, j, k, n]
@inbounds V2 = Fp[i-3, j, k, n]
@inbounds V3 = Fp[i-2, j, k, n]
@inbounds V4 = Fp[i-1, j, k, n]
@inbounds V5 = Fp[i, j, k, n]
@inbounds V6 = Fp[i+1, j, k, n]
@inbounds V7 = Fp[i+2, j, k, n]
fp = c1*V1 + c2*V2 + c3*V3 + c4*V4 + c5*V5 + c6*V6 + c7*V7
@inbounds V1 = Fm[i-3, j, k, n]
@inbounds V2 = Fm[i-2, j, k, n]
@inbounds V3 = Fm[i-1, j, k, n]
@inbounds V4 = Fm[i, j, k, n]
@inbounds V5 = Fm[i+1, j, k, n]
@inbounds V6 = Fm[i+2, j, k, n]
@inbounds V7 = Fm[i+3, j, k, n]
fm = c7*V1 + c6*V2 + c5*V3 + c4*V4 + c3*V5 + c2*V6 + c1*V7
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
elseif ϕx < hybrid_ϕ2
for n = 1:NV
@inbounds V1 = Fp[i-3, j, k, n]
@inbounds V2 = Fp[i-2, j, k, n]
@inbounds V3 = Fp[i-1, j, k, n]
@inbounds V4 = Fp[i, j, k, n]
@inbounds V5 = Fp[i+1, j, k, n]
# FP
s11 = tmp1*(V1-2*V2+V3)^2 + 0.25*(V1-4*V2+3*V3)^2
s22 = tmp1*(V2-2*V3+V4)^2 + 0.25*(V2-V4)^2
s33 = tmp1*(V3-2*V4+V5)^2 + 0.25*(3*V3-4*V4+V5)^2
# s11 = 0.1/(WENOϵ+s11)^2
# s22 = 0.6/(WENOϵ+s22)^2
# s33 = 0.3/(WENOϵ+s33)^2
τ = abs(s11-s33)
s11 = (1 + (τ/(WENOϵ+s11))^2) * 1
s22 = (1 + (τ/(WENOϵ+s22))^2) * 6
s33 = (1 + (τ/(WENOϵ+s33))^2) * 3
invsum = 1/(s11+s22+s33)
v1 = 2*V1-7*V2+11*V3
v2 = -V2+5*V3+2*V4
v3 = 2*V3+5*V4-V5
fp = tmp2*invsum*(s11*v1+s22*v2+s33*v3)
@inbounds V1 = Fm[i-2, j, k, n]
@inbounds V2 = Fm[i-1, j, k, n]
@inbounds V3 = Fm[i, j, k, n]
@inbounds V4 = Fm[i+1, j, k, n]
@inbounds V5 = Fm[i+2, j, k, n]
# FM
s11 = tmp1*(V5-2*V4+V3)^2 + 0.25*(V5-4*V4+3*V3)^2
s22 = tmp1*(V2-2*V3+V4)^2 + 0.25*(V4-V2)^2
s33 = tmp1*(V3-2*V2+V1)^2 + 0.25*(3*V3-4*V2+V1)^2
# s11 = 0.1/(WENOϵ+s11)^2
# s22 = 0.6/(WENOϵ+s22)^2
# s33 = 0.3/(WENOϵ+s33)^2
τ = abs(s11-s33)
s11 = (1 + (τ/(WENOϵ+s11))^2) * 1
s22 = (1 + (τ/(WENOϵ+s22))^2) * 6
s33 = (1 + (τ/(WENOϵ+s33))^2) * 3
invsum = 1/(s11+s22+s33)
v1 = 11*V3-7*V4+2*V5
v2 = -V4+5*V3+2*V2
v3 = 2*V3+5*V2-V1
fm = tmp2*invsum*(s11*v1+s22*v2+s33*v3)
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
else
for n = 1:NV
@inbounds fp = Fp[i-1, j, k, n] + 0.5*minmod(Fp[i, j, k, n] - Fp[i-1, j, k, n],
Fp[i-1, j, k, n] - Fp[i-2, j, k, n])
@inbounds fm = Fm[i, j, k, n] - 0.5*minmod(Fm[i+1, j, k, n] - Fm[i, j, k, n],
Fm[i, j, k, n] - Fm[i-1, j, k, n])
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
end
return
end
#Range: 1 -> N+1
function WENO_y(F, ϕ, Fp, Fm, NV, tag)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG || j > Ny+NG+1 || k > Nz+NG || i < 1+NG || j < 1+NG || k < 1+NG
return
end
if tag[i, j, k] == 1
return
end
tmp1::Float64 = 13/12
tmp2::Float64 = 1/6
c1::Float64 = UP7[1]
c2::Float64 = UP7[2]
c3::Float64 = UP7[3]
c4::Float64 = UP7[4]
c5::Float64 = UP7[5]
c6::Float64 = UP7[6]
c7::Float64 = UP7[7]
# Jameson sensor
@inbounds ϕy = max(ϕ[i, j-1, k], ϕ[i, j, k])
if ϕy < hybrid_ϕ1
for n = 1:NV
@inbounds V1 = Fp[i, j-4, k, n]
@inbounds V2 = Fp[i, j-3, k, n]
@inbounds V3 = Fp[i, j-2, k, n]
@inbounds V4 = Fp[i, j-1, k, n]
@inbounds V5 = Fp[i, j, k, n]
@inbounds V6 = Fp[i, j+1, k, n]
@inbounds V7 = Fp[i, j+2, k, n]
fp = c1*V1 + c2*V2 + c3*V3 + c4*V4 + c5*V5 + c6*V6 + c7*V7
@inbounds V1 = Fm[i, j-3, k, n]
@inbounds V2 = Fm[i, j-2, k, n]
@inbounds V3 = Fm[i, j-1, k, n]
@inbounds V4 = Fm[i, j, k, n]
@inbounds V5 = Fm[i, j+1, k, n]
@inbounds V6 = Fm[i, j+2, k, n]
@inbounds V7 = Fm[i, j+3, k, n]
fm = c7*V1 + c6*V2 + c5*V3 + c4*V4 + c3*V5 + c2*V6 + c1*V7
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
elseif ϕy < hybrid_ϕ2
for n = 1:NV
@inbounds V1 = Fp[i, j-3, k, n]
@inbounds V2 = Fp[i, j-2, k, n]
@inbounds V3 = Fp[i, j-1, k, n]
@inbounds V4 = Fp[i, j, k, n]
@inbounds V5 = Fp[i, j+1, k, n]
# FP
s11 = tmp1*(V1-2*V2+V3)^2 + 0.25*(V1-4*V2+3*V3)^2
s22 = tmp1*(V2-2*V3+V4)^2 + 0.25*(V2-V4)^2
s33 = tmp1*(V3-2*V4+V5)^2 + 0.25*(3*V3-4*V4+V5)^2
# s11 = 0.1/(WENOϵ+s11)^2
# s22 = 0.6/(WENOϵ+s22)^2
# s33 = 0.3/(WENOϵ+s33)^2
τ = abs(s11-s33)
s11 = (1 + (τ/(WENOϵ+s11))^2) * 1
s22 = (1 + (τ/(WENOϵ+s22))^2) * 6
s33 = (1 + (τ/(WENOϵ+s33))^2) * 3
invsum = 1/(s11+s22+s33)
v1 = 2*V1-7*V2+11*V3
v2 = -V2+5*V3+2*V4
v3 = 2*V3+5*V4-V5
fp = tmp2*invsum*(s11*v1+s22*v2+s33*v3)
@inbounds V1 = Fm[i, j-2, k, n]
@inbounds V2 = Fm[i, j-1, k, n]
@inbounds V3 = Fm[i, j, k, n]
@inbounds V4 = Fm[i, j+1, k, n]
@inbounds V5 = Fm[i, j+2, k, n]
# FM
s11 = tmp1*(V5-2*V4+V3)^2 + 0.25*(V5-4*V4+3*V3)^2
s22 = tmp1*(V2-2*V3+V4)^2 + 0.25*(V4-V2)^2
s33 = tmp1*(V3-2*V2+V1)^2 + 0.25*(3*V3-4*V2+V1)^2
# s11 = 0.1/(WENOϵ+s11)^2
# s22 = 0.6/(WENOϵ+s22)^2
# s33 = 0.3/(WENOϵ+s33)^2
τ = abs(s11-s33)
s11 = (1 + (τ/(WENOϵ+s11))^2) * 1
s22 = (1 + (τ/(WENOϵ+s22))^2) * 6
s33 = (1 + (τ/(WENOϵ+s33))^2) * 3
invsum = 1/(s11+s22+s33)
v1 = 11*V3-7*V4+2*V5
v2 = -V4+5*V3+2*V2
v3 = 2*V3+5*V2-V1
fm = tmp2*invsum*(s11*v1+s22*v2+s33*v3)
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
else
for n = 1:NV
@inbounds fp = Fp[i, j-1, k, n] + 0.5*minmod(Fp[i, j, k, n] - Fp[i, j-1, k, n],
Fp[i, j-1, k, n] - Fp[i, j-2, k, n])
@inbounds fm = Fm[i, j, k, n] - 0.5*minmod(Fm[i, j+1, k, n] - Fm[i, j, k, n],
Fm[i, j, k, n] - Fm[i, j-1, k, n])
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
end
return
end
#Range: 1 -> N+1
function WENO_z(F, ϕ, Fp, Fm, NV, tag)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG || j > Ny+NG || k > Nz+NG+1 || i < 1+NG || j < 1+NG || k < 1+NG
return
end
if tag[i, j, k] == 1
return
end
tmp1::Float64 = 13/12
tmp2::Float64 = 1/6
c1::Float64 = UP7[1]
c2::Float64 = UP7[2]
c3::Float64 = UP7[3]
c4::Float64 = UP7[4]
c5::Float64 = UP7[5]
c6::Float64 = UP7[6]
c7::Float64 = UP7[7]
# Jameson sensor
@inbounds ϕz = max(ϕ[i, j, k-1], ϕ[i, j, k])
if ϕz < hybrid_ϕ1
for n = 1:NV
@inbounds V1 = Fp[i, j, k-4, n]
@inbounds V2 = Fp[i, j, k-3, n]
@inbounds V3 = Fp[i, j, k-2, n]
@inbounds V4 = Fp[i, j, k-1, n]
@inbounds V5 = Fp[i, j, k, n]
@inbounds V6 = Fp[i, j, k+1, n]
@inbounds V7 = Fp[i, j, k+2, n]
fp = c1*V1 + c2*V2 + c3*V3 + c4*V4 + c5*V5 + c6*V6 + c7*V7
@inbounds V1 = Fm[i, j, k-3, n]
@inbounds V2 = Fm[i, j, k-2, n]
@inbounds V3 = Fm[i, j, k-1, n]
@inbounds V4 = Fm[i, j, k, n]
@inbounds V5 = Fm[i, j, k+1, n]
@inbounds V6 = Fm[i, j, k+2, n]
@inbounds V7 = Fm[i, j, k+3, n]
fm = c7*V1 + c6*V2 + c5*V3 + c4*V4 + c3*V5 + c2*V6 + c1*V7
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
elseif ϕz < hybrid_ϕ2
for n = 1:NV
@inbounds V1 = Fp[i, j, k-3, n]
@inbounds V2 = Fp[i, j, k-2, n]
@inbounds V3 = Fp[i, j, k-1, n]
@inbounds V4 = Fp[i, j, k, n]
@inbounds V5 = Fp[i, j, k+1, n]
# FP
s11 = tmp1*(V1-2*V2+V3)^2 + 0.25*(V1-4*V2+3*V3)^2
s22 = tmp1*(V2-2*V3+V4)^2 + 0.25*(V2-V4)^2
s33 = tmp1*(V3-2*V4+V5)^2 + 0.25*(3*V3-4*V4+V5)^2
# s11 = 0.1/(WENOϵ+s11)^2
# s22 = 0.6/(WENOϵ+s22)^2
# s33 = 0.3/(WENOϵ+s33)^2
τ = abs(s11-s33)
s11 = (1 + (τ/(WENOϵ+s11))^2) * 1
s22 = (1 + (τ/(WENOϵ+s22))^2) * 6
s33 = (1 + (τ/(WENOϵ+s33))^2) * 3
invsum = 1/(s11+s22+s33)
v1 = 2*V1-7*V2+11*V3
v2 = -V2+5*V3+2*V4
v3 = 2*V3+5*V4-V5
fp = tmp2*invsum*(s11*v1+s22*v2+s33*v3)
@inbounds V1 = Fm[i, j, k-2, n]
@inbounds V2 = Fm[i, j, k-1, n]
@inbounds V3 = Fm[i, j, k, n]
@inbounds V4 = Fm[i, j, k+1, n]
@inbounds V5 = Fm[i, j, k+2, n]
# FM
s11 = tmp1*(V5-2*V4+V3)^2 + 0.25*(V5-4*V4+3*V3)^2
s22 = tmp1*(V2-2*V3+V4)^2 + 0.25*(V4-V2)^2
s33 = tmp1*(V3-2*V2+V1)^2 + 0.25*(3*V3-4*V2+V1)^2
# s11 = 0.1/(WENOϵ+s11)^2
# s22 = 0.6/(WENOϵ+s22)^2
# s33 = 0.3/(WENOϵ+s33)^2
τ = abs(s11-s33)
s11 = (1 + (τ/(WENOϵ+s11))^2) * 1
s22 = (1 + (τ/(WENOϵ+s22))^2) * 6
s33 = (1 + (τ/(WENOϵ+s33))^2) * 3
invsum = 1/(s11+s22+s33)
v1 = 11*V3-7*V4+2*V5
v2 = -V4+5*V3+2*V2
v3 = 2*V3+5*V2-V1
fm = tmp2*invsum*(s11*v1+s22*v2+s33*v3)
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
else
for n = 1:NV
@inbounds fp = Fp[i, j, k-1, n] + 0.5*minmod(Fp[i, j, k, n] - Fp[i, j, k-1, n],
Fp[i, j, k-1, n] - Fp[i, j, k-2, n])
@inbounds fm = Fm[i, j, k, n] - 0.5*minmod(Fm[i, j, k+1, n] - Fm[i, j, k, n],
Fm[i, j, k, n] - Fm[i, j, k-1, n])
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
end
return
end
function TENO_x(F, Fp, Fm, NV, tag)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG+1 || j > Ny+NG || k > Nz+NG || i < 1+NG || j < 1+NG || k < 1+NG
return
end
if tag[i, j, k] == 1
return
end
oneSix::Float64 = 1/6
for n = 1:NV
@inbounds V1 = Fp[i-3, j, k, n]
@inbounds V2 = Fp[i-2, j, k, n]
@inbounds V3 = Fp[i-1, j, k, n]
@inbounds V4 = Fp[i, j, k, n]
@inbounds V5 = Fp[i+1, j, k, n]
# FP
s11 = 13*(V1-2*V2+V3)^2 + 3*(V1-4*V2+3*V3)^2
s22 = 13*(V2-2*V3+V4)^2 + 3*(V2-V4)^2
s33 = 13*(V3-2*V4+V5)^2 + 3*(3*V3-4*V4+V5)^2
τ = abs(s11-s33)
@fastmath a1 = (1 + τ/(s11+TENOϵ))^6
@fastmath a2 = (1 + τ/(s22+TENOϵ))^6
@fastmath a3 = (1 + τ/(s33+TENOϵ))^6
invsum = 1/(a1+a2+a3)
a1 = 1*((a1*invsum)<TENOct ? 0.0 : 1.0)
a2 = 6*((a2*invsum)<TENOct ? 0.0 : 1.0)
a3 = 3*((a3*invsum)<TENOct ? 0.0 : 1.0)
v1 = 2*V1-7*V2+5*V3
v2 = -V2-V3+2*V4
v3 = -4*V3+5*V4-V5
invsum = 1/(a1+a2+a3)
fp = V3+oneSix*invsum*(a1*v1+a2*v2+a3*v3)
@inbounds V1 = Fm[i-2, j, k, n]
@inbounds V2 = Fm[i-1, j, k, n]
@inbounds V3 = Fm[i, j, k, n]
@inbounds V4 = Fm[i+1, j, k, n]
@inbounds V5 = Fm[i+2, j, k, n]
# FM
s11 = 13*(V5-2*V4+V3)^2 + 3*(V5-4*V4+3*V3)^2
s22 = 13*(V2-2*V3+V4)^2 + 3*(V4-V2)^2
s33 = 13*(V3-2*V2+V1)^2 + 3*(3*V3-4*V2+V1)^2
τ = abs(s11-s33)
@fastmath a1 = (1 + τ/(s11+TENOϵ))^6
@fastmath a2 = (1 + τ/(s22+TENOϵ))^6
@fastmath a3 = (1 + τ/(s33+TENOϵ))^6
invsum = 1/(a1+a2+a3)
a1 = 1*((a1*invsum)<TENOct ? 0.0 : 1.0)
a2 = 6*((a2*invsum)<TENOct ? 0.0 : 1.0)
a3 = 3*((a3*invsum)<TENOct ? 0.0 : 1.0)
v1 = 5*V3-7*V4+2*V5
v2 = -V4-V3+2*V2
v3 = -4*V3+5*V2-V1
invsum = 1/(a1+a2+a3)
fm = V3+oneSix*invsum*(a1*v1+a2*v2+a3*v3)
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
return
end
function TENO_y(F, Fp, Fm, NV, tag)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG || j > Ny+NG+1 || k > Nz+NG || i < 1+NG || j < 1+NG || k < 1+NG
return
end
if tag[i, j, k] == 1
return
end
oneSix::Float64 = 1/6
for n = 1:NV
@inbounds V1 = Fp[i, j-3, k, n]
@inbounds V2 = Fp[i, j-2, k, n]
@inbounds V3 = Fp[i, j-1, k, n]
@inbounds V4 = Fp[i, j, k, n]
@inbounds V5 = Fp[i, j+1, k, n]
# FP
s11 = 13*(V1-2*V2+V3)^2 + 3*(V1-4*V2+3*V3)^2
s22 = 13*(V2-2*V3+V4)^2 + 3*(V2-V4)^2
s33 = 13*(V3-2*V4+V5)^2 + 3*(3*V3-4*V4+V5)^2
τ = abs(s11-s33)
@fastmath a1 = (1 + τ/(s11+TENOϵ))^6
@fastmath a2 = (1 + τ/(s22+TENOϵ))^6
@fastmath a3 = (1 + τ/(s33+TENOϵ))^6
invsum = 1/(a1+a2+a3)
a1 = 1*((a1*invsum)<TENOct ? 0.0 : 1.0)
a2 = 6*((a2*invsum)<TENOct ? 0.0 : 1.0)
a3 = 3*((a3*invsum)<TENOct ? 0.0 : 1.0)
v1 = 2*V1-7*V2+5*V3
v2 = -V2-V3+2*V4
v3 = -4*V3+5*V4-V5
invsum = 1/(a1+a2+a3)
fp = V3+oneSix*invsum*(a1*v1+a2*v2+a3*v3)
@inbounds V1 = Fm[i, j-2, k, n]
@inbounds V2 = Fm[i, j-1, k, n]
@inbounds V3 = Fm[i, j, k, n]
@inbounds V4 = Fm[i, j+1, k, n]
@inbounds V5 = Fm[i, j+2, k, n]
# FM
s11 = 13*(V5-2*V4+V3)^2 + 3*(V5-4*V4+3*V3)^2
s22 = 13*(V2-2*V3+V4)^2 + 3*(V4-V2)^2
s33 = 13*(V3-2*V2+V1)^2 + 3*(3*V3-4*V2+V1)^2
τ = abs(s11-s33)
@fastmath a1 = (1 + τ/(s11+TENOϵ))^6
@fastmath a2 = (1 + τ/(s22+TENOϵ))^6
@fastmath a3 = (1 + τ/(s33+TENOϵ))^6
invsum = 1/(a1+a2+a3)
a1 = 1*((a1*invsum)<TENOct ? 0.0 : 1.0)
a2 = 6*((a2*invsum)<TENOct ? 0.0 : 1.0)
a3 = 3*((a3*invsum)<TENOct ? 0.0 : 1.0)
v1 = 5*V3-7*V4+2*V5
v2 = -V4-V3+2*V2
v3 = -4*V3+5*V2-V1
invsum = 1/(a1+a2+a3)
fm = V3+oneSix*invsum*(a1*v1+a2*v2+a3*v3)
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
return
end
function TENO_z(F, Fp, Fm, NV, tag)
i = (blockIdx().x-1i32)* blockDim().x + threadIdx().x
j = (blockIdx().y-1i32)* blockDim().y + threadIdx().y
k = (blockIdx().z-1i32)* blockDim().z + threadIdx().z
if i > Nxp+NG || j > Ny+NG || k > Nz+NG+1 || i < 1+NG || j < 1+NG || k < 1+NG
return
end
if tag[i, j, k] == 1
return
end
oneSix::Float64 = 1/6
for n = 1:NV
@inbounds V1 = Fp[i, j, k-3, n]
@inbounds V2 = Fp[i, j, k-2, n]
@inbounds V3 = Fp[i, j, k-1, n]
@inbounds V4 = Fp[i, j, k, n]
@inbounds V5 = Fp[i, j, k+1, n]
# FP
s11 = 13*(V1-2*V2+V3)^2 + 3*(V1-4*V2+3*V3)^2
s22 = 13*(V2-2*V3+V4)^2 + 3*(V2-V4)^2
s33 = 13*(V3-2*V4+V5)^2 + 3*(3*V3-4*V4+V5)^2
τ = abs(s11-s33)
@fastmath a1 = (1 + τ/(s11+TENOϵ))^6
@fastmath a2 = (1 + τ/(s22+TENOϵ))^6
@fastmath a3 = (1 + τ/(s33+TENOϵ))^6
invsum = 1/(a1+a2+a3)
a1 = 1*((a1*invsum)<TENOct ? 0.0 : 1.0)
a2 = 6*((a2*invsum)<TENOct ? 0.0 : 1.0)
a3 = 3*((a3*invsum)<TENOct ? 0.0 : 1.0)
v1 = 2*V1-7*V2+5*V3
v2 = -V2-V3+2*V4
v3 = -4*V3+5*V4-V5
invsum = 1/(a1+a2+a3)
fp = V3+oneSix*invsum*(a1*v1+a2*v2+a3*v3)
@inbounds V1 = Fm[i, j, k-2, n]
@inbounds V2 = Fm[i, j, k-1, n]
@inbounds V3 = Fm[i, j, k, n]
@inbounds V4 = Fm[i, j, k+1, n]
@inbounds V5 = Fm[i, j, k+2, n]
# FM
s11 = 13*(V5-2*V4+V3)^2 + 3*(V5-4*V4+3*V3)^2
s22 = 13*(V2-2*V3+V4)^2 + 3*(V4-V2)^2
s33 = 13*(V3-2*V2+V1)^2 + 3*(3*V3-4*V2+V1)^2
τ = abs(s11-s33)
@fastmath a1 = (1 + τ/(s11+TENOϵ))^6
@fastmath a2 = (1 + τ/(s22+TENOϵ))^6
@fastmath a3 = (1 + τ/(s33+TENOϵ))^6
invsum = 1/(a1+a2+a3)
a1 = 1*((a1*invsum)<TENOct ? 0.0 : 1.0)
a2 = 6*((a2*invsum)<TENOct ? 0.0 : 1.0)
a3 = 3*((a3*invsum)<TENOct ? 0.0 : 1.0)
v1 = 5*V3-7*V4+2*V5
v2 = -V4-V3+2*V2
v3 = -4*V3+5*V2-V1
invsum = 1/(a1+a2+a3)
fm = V3+oneSix*invsum*(a1*v1+a2*v2+a3*v3)
@inbounds F[i-NG, j-NG, k-NG, n] = fp + fm
end
return
end