def taylor_green():
tf = 10
Lx = 2 * pi
Ly = 2 * pi
nx = 50
ny = 50
γ = 1.4
ρ = 1
p = 100 / γ
A = eye(3)
MP = material_params(EOS='sg', ρ0=ρ, cv=1, γ=γ, b0=10, μ=1e-2)
dX = [Lx / nx, Ly / ny]
u = zeros([nx, ny, 14])
for i in range(nx):
for j in range(ny):
x = (i + 0.5) * dX[0]
y = (j + 0.5) * dX[1]
v = array([sin(x) * cos(y), -cos(x) * sin(y)])
pi = p + (cos(2 * x) + cos(2 * y)) / 4
u[i, j] = Cvec(ρ, pi, v, MP, A)
print("TAYLOR-GREEN VORTEX")
return u, [MP], tf, dX
def boundary_layer():
tf = 10
Lx = 1.5
Ly = 0.4
nx = 75
ny = 100
γ = 1.4
ρ = 1
p = 100 / γ
v = array([1, 0, 0])
A = eye(3)
MP = material_params(EOS='sg', ρ0=ρ, cv=1, γ=γ, b0=8, μ=1e-3)
u = zeros([nx, ny, 14])
Q = Cvec(ρ, p, v, MP, A)
for i in range(nx):
for j in range(ny):
u[i, j] = Q
print("LAMINAR BOUNDARY LAYER")
return u, [MP], tf, [Lx / nx, Ly / ny], ''
def convected_vortex(μ=1e-6, κ=1e-6, t=0):
tf = 1
Lx = 10
Ly = 10
nx = 10
ny = 10
ε = 5
γ = 1.4
ρ = 1
p = 1
v = array([1, 1, 0])
J = zeros(3)
dX = [Lx / nx, Ly / ny]
MP = material_params(EOS='sg', ρ0=ρ, cv=2.5, γ=γ, b0=0.5, cα=1, μ=μ, κ=κ)
u = zeros([nx, ny, 17])
for i in range(nx):
for j in range(ny):
x = (i + 0.5) * dX[0]
y = (j + 0.5) * dX[1]
dv, dT, dρ, dp, A = vortex(x, y, Lx / 2 + t, Ly / 2 + t, ε, γ, ρ)
u[i, j] = Cvec(ρ + dρ, p + dp, v + dv, MP, A, J)
print("CONVECTED ISENTROPIC VORTEX")
return u, [MP], tf, dX, 'periodic'
def double_shear_layer():
tf = 1.8
Lx = 1
Ly = 1
nx = 200
ny = 200
γ = 1.4
ρ = 1
p = 100 / γ
A = eye(3)
MP = material_params(EOS='sg', ρ0=ρ, cv=1, γ=γ, b0=8, μ=2e-4)
dX = [Lx / nx, Ly / ny]
ρ_ = 30
δ = 0.05
u = zeros([nx, ny, 14])
for i in range(nx):
for j in range(ny):
x = (i + 0.5) * dX[0]
y = (j + 0.5) * dX[1]
if y > 0.75:
v1 = tanh(ρ_ * (0.75 - y))
else:
v1 = tanh(ρ_ * (y - 0.25))
v2 = δ * sin(2 * pi * x)
v = array([v1, v2, 0])
u[i, j] = Cvec(ρ, p, v, MP, A)
print("DOUBLE SHEAR LAYER")
return u, [MP], tf, dX
def viscous_shock(center=0):
""" 10.1016/j.jcp.2016.02.015
4.13 Viscous shock profile
"""
tf = 0.2
nx = 100
Lx = 1
Ms = 2
γ = 1.4
μ = 2e-2
MP = material_params(EOS='sg', ρ0=1, cv=2.5, γ=γ, b0=5, cα=5, μ=μ, Pr=0.75)
dX = [Lx / nx]
x = arange(-Lx / 2, Lx / 2, 1 / nx)
ρ = zeros(nx)
p = zeros(nx)
v = zeros(nx)
for i in range(nx):
ρ[i], p[i], v[i] = viscous_shock_exact(x[i], Ms, MP, μ, center=center)
v -= v[0] # Velocity in shock 0
u = zeros([nx, 17])
for i in range(nx):
A = (ρ[i])**(1 / 3) * eye(3)
J = zeros(3)
u[i] = Cvec(ρ[i], p[i], array([v[i], 0, 0]), MP, A, J)
return u, [MP], tf, dX, 'transitive'
def heat_conduction(isMulti=False):
""" 10.1016/j.jcp.2016.02.015
4.12 Heat conduction in a gas
"""
tf = 1
nx = 200
Lx = 1
MPs = [
material_params(EOS='sg',
ρ0=1,
cv=2.5,
γ=1.4,
b0=1,
cα=2,
μ=1e-2,
κ=1e-2)
]
if isMulti:
MPs = 2 * MPs
ρL = 2
pL = 1
vL = zeros(3)
ρR = 0.5
pR = 1
vR = zeros(3)
dX = [Lx / nx]
u = primitive_IC(nx, dX, ρL, pL, vL, ρR, pR, vR, MPs)
return u, MPs, tf, dX, 'transitive'
def shock_detonation():
tf = 0.5
L = 1
nx = 400
MP = material_params('sg',
ρ0=1,
γ=1.4,
cv=2.5,
b0=1e-8,
μ=1e-4,
Qc=1,
Kc=250,
Ti=0.25,
REACTION='d')
ρL = 1.4
pL = 1
vL = zeros(3)
AL = ρL**(1 / 3) * eye(3)
λL = 0
ρR = 0.887565
pR = 0.191709
vR = array([-0.57735, 0, 0])
AR = ρR**(1 / 3) * eye(3)
λR = 1
QL = Cvec(ρL, pL, vL, MP, A=AL, λ=λL)
QR = Cvec(ρR, pR, vR, MP, A=AR, λ=λR)
u = zeros([nx, 15])
for i in range(nx):
if i < nx / 4:
u[i] = QL
else:
u[i] = QR
return u, [MP], tf, [L / nx], 'transitive'
def circular_explosion():
tf = 0.2
Lx = 2
Ly = 2
nx = 400
ny = 400
R = 0.25 * Lx
MP = material_params(EOS='sg', ρ0=1, cv=2.5, γ=1.4,
b0=0.5, cα=0.5, μ=1e-4, κ=1e-4)
dX = [Lx / nx, Ly / ny]
v = zeros([3])
J = zeros([3])
ρi = 1
pi = 1
Ai = eye(3)
Qi = Cvec(ρi, pi, v, MP, Ai, J)
ρo = 0.125
po = 0.1
Ao = 0.5 * eye(3)
Qo = Cvec(ρo, po, v, MP, Ao, J)
u = zeros([nx, ny, 17])
for i in range(nx):
for j in range(ny):
x = -Lx / 2 + (i + 0.5) * dX[0]
y = -Ly / 2 + (j + 0.5) * dX[1]
r = sqrt(x**2 + y**2)
if r < R:
u[i, j] = Qi
else:
u[i, j] = Qo
print("CIRCULAR EXPLOSION")
return u, [MP], tf, dX, 'transitive'
def stokes(isMulti=False):
""" 10.1016/j.jcp.2016.02.015
4.3 The first problem of Stokes
"""
tf = 1
nx = 200
Lx = 1
γ = 1.4
μ = 1e-2 # 1e-3 # 1e-4
MPs = [
material_params(EOS='sg',
ρ0=1,
cv=1,
γ=γ,
b0=1,
cα=1e-16,
μ=μ,
Pr=0.75)
]
if isMulti:
MPs = 2 * MPs
ρL = 1
pL = 1 / γ
vL = array([0, -0.1, 0])
ρR = 1
pR = 1 / γ
vR = array([0, 0.1, 0])
dX = [Lx / nx]
u = primitive_IC(nx, dX, ρL, pL, vL, ρR, pR, vR, MPs)
return u, MPs, tf, dX, 'transitive'
def dΧ(xh, dt):
""" returns dΧ/dx and dΧ/dt at spatial node i and temporal node j
"""
dxdΧ = dot(DERVALS, xh)
dxdτ = dot(xh, DERVALS.T)
dΧdx = 1 / dxdΧ
dΧdt = -dxdτ / (dxdΧ * dt)
return dΧdx, dΧdt
if __name__ == "__main__":
MP = material_params(EOS='sg',
ρ0=1,
cv=1,
γ=1.4,
b0=1,
cα=1,
μ=1e-2,
Pr=0.75)
"""
ρL = 1
pL = 1
vL = zeros(3)
AL = ρL**(1/3) * eye(3)
JL = zeros(3)
MPL = MP
ρR = 0.1
pR = 0.1
vR = zeros(3)
AR = ρR**(1/3) * eye(3)
ε = rand(3, 3)
ε -= 0.5
ε *= 2
Λ = rand(3)
else:
ε = array([[0.62, 0.40, 1.14], [-0.28, -1.41, 0.59], [-0.19, -0.72,
-1.28]])
Λ = ones(3)
τ = 1.45e-9
tScale = 10
includeSources = 1
n = 50
PAR = material_params('sg', 1, γ=1.4, b0=1, τ0=τ)
### Auxiliary Functions ###
def sgn(x):
if x >= 0:
return 1
else:
return -1
def sec(x):
return 1 / lim(cos(x))
from gpr.misc.objects import material_params
""" SI Units """
TNT_JWL_SI = material_params(EOS='jwl',
ρ0=1840,
cv=815,
Γ0=0.25,
A=854.5e9,
B=20.5e9,
R1=4.6,
R2=1.35,
b0=2100)
PBX_SG_SI = material_params(EOS='sg', ρ0=1840, γ=2.85, b0=1, μ=1e-2)
C4_JWL_SI = material_params(EOS='jwl',
ρ0=1601,
cv=2.487e6 / 1601,
Γ0=0.8938,
A=7.781e13,
B=-5.031e9,
R1=11.3,
R2=1.13,
b0=1487,
REACTION='i',
Qc=9e9 / 1601,
I=4e6,
G1=1.4e-20,
G2=0,
a=0.0367,
b=2 / 3,
from gpr.misc.objects import material_params, hyperelastic_params
# TODO: convert all tests from CGS to SI
""" Hyperelastic """
Cu_HYP_SI = hyperelastic_params(ρ0=8930, α=1, β=3, γ=2, cv=390,
T0=300, b0=2141, c0=4651)
Al_HYP_CGS = hyperelastic_params(ρ0=2.71, α=1, β=3.577, γ=2.088, cv=9e-4,
T0=300, b0=3.16, c0=6.22)
Cu_HYP_CGS = hyperelastic_params(ρ0=8.9, α=1, β=3, γ=2, cv=4e-4,
T0=300, b0=2.1, c0=4.6)
""" Other """
VAC = material_params(EOS='vac', ρ0=0)
from gpr.misc.objects import material_params
""" SI Units """
Al_GRP_SI = material_params(EOS='gr',
ρ0=2710,
cv=900,
Tref=300,
c0=5037,
α=1,
β=3.577,
γ=2.088,
b0=3160,
σY=0.4e9,
τ0=1,
n=100)
Cu_SMGP_SI = material_params(EOS='smg',
ρ0=8930,
cv=390,
c0=3939,
Γ0=2,
s=1.5,
b0=2244,
σY=9e7,
τ0=1,
n=100)
Cu_GR_SI = material_params(EOS='gr',
ρ0=8930,
cv=390,
Tref=300,
from gpr.misc.objects import material_params
""" SI Units """
Air_SG_SI = material_params(EOS='sg',
ρ0=1.18,
cv=718,
γ=1.4,
b0=50,
cα=50,
μ=1.85e-5,
Pr=0.714)
He_SG_SI = material_params(EOS='sg',
ρ0=0.163,
cv=3127,
γ=5 / 3,
b0=1,
cα=1,
μ=1.99e-5,
Pr=0.688)
H20_SG_SI = material_params(EOS='sg',
ρ0=997,
cv=950,
γ=4.4,
pINF=6e8,
b0=1,
cα=1,
μ=1e-3,
Pr=7)
