def pop_plot():
""" 10.1016/j.jcp.2018.03.037
5.3. C4 Pop-plot
"""
tf = 1e-7
nx = 2000
Lx = 6.4e-2
L0 = 0.04e-2
MP = C4_JWL_SI
ρ = 1590
p = 1e5
pb = 30e9
v = zeros(3)
A = eye(3)
Q = Cvec(ρ, p, v, MP, A, λ=1)
Qb = Cvec(ρ, pb, v, MP, A, λ=0)
dX = [Lx / nx]
u = zeros([nx, 15])
for i in range(nx):
x = (i + 0.5) * dX[0]
if x < L0:
u[i] = Qb
else:
u[i] = Q
return u, [MP], tf, dX, 'transitive'
def primitive_IC(nx,
dX,
ρL,
pL,
vL,
ρR,
pR,
vR,
MPs,
x0=0.5,
λL=None,
λR=None):
isMulti = len(MPs) > 1
MPL = MPs[0]
MPR = MPs[1] if isMulti else MPL
AL = (ρL / MPL.ρ0)**(1 / 3) * eye(3)
JL = zeros(3)
QL = Cvec(ρL, pL, vL, MPL, AL, JL, λL)
AR = (ρR / MPR.ρ0)**(1 / 3) * eye(3)
JR = zeros(3)
QR = Cvec(ρR, pR, vR, MPR, AR, JR, λR)
return riemann_IC(nx, dX, QL, QR, x0, isMulti)
def aluminium_plates():
""" N = 2
cfl = 0.8
SPLIT = True
FLUX = 0
LSET = 2
RIEMANN_STICK = false
RIEMANN_RELAXATION = true
STAR_TOL = 1e-8
"""
MP = Al_GRP_SI
Lx = 0.03
Ly = 0.04
nx = 300
ny = 400
tf = 5e-6
ρ = MP.ρ0
p = 0
v0 = array([400., 0., 0.])
v1 = zeros(3)
A = eye(3)
MPs = [VAC, MP, MP]
dX = [Lx / nx, Ly / ny]
Q0 = pad(Cvec(ρ, p, v0, MP, A), (0, 2), 'constant')
Q1 = pad(Cvec(ρ, p, v1, MP, A), (0, 2), 'constant')
u = zeros([nx, ny, 16])
for i in range(nx):
for j in range(ny):
x = (i+0.5) * dX[0]
y = (j+0.5) * dX[1]
# projectile
if 0.001 <= x <= 0.006 and 0.014 <= y <= 0.026:
u[i, j] = Q0
u[i, j, -2] = 1
u[i, j, -1] = -1
# plate
elif 0.006 <= x <= 0.028 and 0.003 <= y <= 0.037:
u[i, j] = Q1
u[i, j, -2] = 1
u[i, j, -1] = 1
# vacuum
else:
u[i, j, -2] = -1
u[i, j, -1] = -1
u = u[:, int(ny/2):]
return u, MPs, tf, dX, 'halfy'
def helium_bubble():
""" 10.1016/j.jcp.2003.10.010
5. Numerical experiments - Test B
N = 3
cfl = 0.5
SPLIT = True
SOLVER = 'rusanov'
"""
#tf = 7e-4
tf = 14e-4
nx = 200
Lx = 1
dX = [Lx / nx]
dx = dX[0]
ρL = 1.3333
pL = 1.5e5
vL = array([35.35 * sqrt(10), 0, 0])
AL = ρL**(1 / 3) * eye(3)
ρM = 1
pM = 1e5
vM = zeros(3)
AM = ρM**(1 / 3) * eye(3)
ρR = 0.1379
pR = 1e5
vR = zeros(3)
AR = ρR**(1 / 3) * eye(3)
u = zeros([nx, 18])
Q1 = Cvec(ρL, pL, vL, Air_SG_SI, AL)
Q2 = Cvec(ρM, pM, vM, Air_SG_SI, AM)
Q3 = Cvec(ρR, pR, vR, He_SG_SI, AR)
for i in range(nx):
if i * dx < 0.05:
u[i] = Q1
elif i * dx < 0.4:
u[i] = Q2
elif i * dx < 0.6:
u[i] = Q3
else:
u[i] = Q2
if i * dx < 0.4 or i * dx >= 0.6:
u[i, -1] = -1
else:
u[i, -1] = 1
return u, [Air_SG_SI, He_SG_SI], tf, dX, 'transitive'
def pbx_copper(test):
""" 10.1016/j.jcp.2011.07.008
6.1 Initial value problems
N = 3
cfl = 0.5
SPLIT = True
FLUX = 0
"""
nx = 3000
Lx = 1
dX = [Lx / nx]
if test == 1:
pL = 18.9e9
vR = zeros(3)
FR = eye(3)
tf = 5e-5
elif test == 2:
pL = 1e5
vR = array([2, 0, 0.1])
FR = array([[1, 0, 0], [-0.01, 0.95, 0.02], [-0.015, 0, 0.9]])
tf = 9e-5
vL = zeros(3)
ρL = 1840
AL = eye(3)
SR = 0
if test == 1:
QL = Cvec(ρL, pL, vL, PBX_SG_SI, AL)
QR = Cvec_hyp(FR, SR, vR, Cu_HYP_SI)
MPs = [PBX_SG_SI, Cu_GR_SI]
elif test == 2:
QL = Cvec_hyp(FR, SR, vR, Cu_HYP_SI)
QR = Cvec(ρL, pL, vL, PBX_SG_SI, AL)
MPs = [Cu_GR_SI, PBX_SG_SI]
QL = concatenate([QL, [0]])
QR = concatenate([QR, [0]])
u = riemann_IC(nx, dX, QL, QR, 0.5, True)
return u, MPs, tf, dX, 'transitive'
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 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 piston():
""" http://arxiv.org/abs/1806.00706
6.1 Elasto-plastic piston
N = 3
cfl = 0.5
SPLIT = True
SOLVER = 'roe'
"""
tf = 1.5e-4
nx = 400
Lx = 1
dX = [Lx / nx]
MP = Cu_SMGP_SI
ρ = MP.ρ0
p = 0
v = zeros(3)
A = eye(3)
Q = Cvec(ρ, p, v, MP, A)
u = zeros([nx, 14])
for i in range(nx):
u[i] = Q
return u, [MP], tf, dX, 'piston_bc'
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 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 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 cylindrical_shock():
""" 10.1002/nme.2695
6.2. Two-dimensional test case
N = 4
cfl = 0.8
SPLIT = True
SOLVER = 'roe'
"""
tf = 10e-6
nx = 500
ny = 500
Lx = 0.2
Ly = 0.2
dX = [Lx / nx, Ly / ny]
MP = Cu_GRP_SI
ρi = MP.ρ0
pi = 0
Ai = eye(3)
ρo = 9375
po = 10e9
Ao = (ρo / MP.ρ0)**(1 / 3) * eye(3)
v = zeros(3)
Qi = Cvec(ρi, pi, v, MP, Ai)
Qo = Cvec(ρo, po, v, MP, Ao)
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]
r = sqrt((x - Lx / 2)**2 + (y - Ly / 2)**2)
if r > 0.02:
u[i, j] = Qo
else:
u[i, j] = Qi
return u[:, 250:], [MP], tf, dX, 'slip'
def steady_znd():
n = 100
MP = NM_JWL_SI
L = 0.0062432
ρ = 1137
p = 23e9
tf = 1e-6
Q = Cvec(ρ, 0, zeros(3), MP, A=eye(3), λ=1)
Qs = Cvec(ρ, p, zeros(3), MP, A=eye(3), λ=1)
u = zeros([n, 15])
for i in range(n):
u[i] = Q
u[0] = Qs
return u, [MP], tf, [L / n], 'transitive'
def generate_vector(MP):
A = rand(3, 3)
A *= sign(det(A))
ρ = det(A) * MP.ρ0
p = rand()
v = rand(3)
J = rand(3)
E = total_energy(ρ, p, v, A, J, 0, MP)
return Cvec(ρ, p, v, A, J, MP)
def generate_vecs(MP):
A = rand(3, 3)
A /= sign(det3(A))
ρ = det3(A) * MP.ρ0
p = rand()
v = rand(3)
J = rand(3)
Q = Cvec(ρ, p, v, MP, A, J)
P = State(Q, MP)
return Q, P
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 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 Wfan(S, P, MP, a):
r = P.ρ
u = P.v[0]
p = P.p()
y = MP.γ
pINF = MP.pINF
temp = 2 / (y + 1) + (y - 1) * (u - S) / ((y + 1) * a)
rf = r * pow(temp, 2 / (y - 1))
vf = array([2 * (a + (y - 1) * u / 2 + S) / (y + 1), 0, 0])
pf = (p + pINF) * pow(temp, 2 * y / (y - 1)) - pINF
return Cvec(rf, pf, vf, MP)
def taylor_bar():
""" N = 2
cfl = 0.8
SPLIT = True
FLUX = 0
LSET = 1
DESTRESS = false
RIEMANN_STICK = false
RIEMANN_RELAXATION = true
STAR_TOL = 1e-8
"""
Lx = 200
Ly = 550
tf = 5e3
nx = 200
ny = int(nx * Ly / Lx)
dX = [Lx / nx, Ly / ny]
p = 0
v = array([0, -0.015, 0])
A = eye(3)
MP = Al_SMGP_CGS
MPs = [VAC, MP]
Q = pad(Cvec(MP.ρ0, p, v, MP, A), (0, 1), 'constant')
u = zeros([nx, ny, 15])
for i in range(nx):
for j in range(ny):
x = (i+0.5) * dX[0]
y = (j+0.5) * dX[1]
# projectile
if Lx / 4 <= x <= 3 * Lx / 4 and y <= 5.5 * Ly / 6:
u[i, j] = Q
u[i, j, -1] = 1
# vacuum
else:
u[i, j, -1] = -1
u = u[int(nx/2):]
return u, MPs, tf, dX, 'halfx'
def rod_penetration():
""" N = 2
cfl = 0.8
SPLIT = True
FLUX = 0
LSET = 2
RIEMANN_RELAXATION = true
"""
D = 0.029
V = -1250
# D = 0.0495
# V = -1700
o = 0.01
nx = 200
Lx = 0.06
Ly = 0.05 + 1.5 * D
ny = int(nx * Ly / Lx)
dX = [Lx / nx, Ly / ny]
tf = 20e-6 # 80e-6
MP1 = W_SMGP_SI
MP2 = Steel_SMGP_SI
p = 0
v1 = array([0, V, 0])
v2 = zeros(3)
A = eye(3)
MPs = [VAC, MP1, MP2]
dX = [Lx / nx, Ly / ny]
Q1 = pad(Cvec(MP1.ρ0, p, v1, MP1, A), (0, 2), 'constant')
Q2 = pad(Cvec(MP2.ρ0, p, v2, MP2, A), (0, 2), 'constant')
u = zeros([nx, ny, 16])
for i in range(nx):
for j in range(ny):
x = (i+0.5) * dX[0]
y = (j+0.5) * dX[1]
# projectile
if 0.028 <= x <= 0.032 and D + o <= y <= D + 0.05 + o:
u[i, j] = Q1
u[i, j, -2] = 1
u[i, j, -1] = -1
# plate
elif o <= y <= D + o:
u[i, j] = Q2
u[i, j, -2] = 1
u[i, j, -1] = 1
# vacuum
else:
u[i, j, -2] = -1
u[i, j, -1] = -1
u = u[int(nx/2):]
return u, MPs, tf, dX, 'halfx'
def exact_euler(n, t, x0, QL, QR, MPL, MPR):
""" Returns the exact solution to the Euler equations at (x,t),
given initial states PL for x<x0 and PR for x>x0
"""
ret = zeros([n, len(QL)])
PL = State(QL, MPL)
PR = State(QR, MPR)
ρL = PL.ρ
ρR = PR.ρ
uL = PL.v[0]
uR = PR.v[0]
pL = PL.p()
pR = PR.p()
c0L = c_0(ρL, pL, eye(3), MPL)
c0R = c_0(ρR, pR, eye(3), MPR)
p_ = p_star(PL, PR, MPL, MPR)
u_ = u_star(p_, PL, PR, MPL, MPR)
print('Interface:', u_ * t + x0)
for i in range(n):
x = (i + 0.5) / n
S = (x - x0) / t
if (S < u_):
if (p_ < pL): # Left fan
if (S < uL - c0L):
ret[i] = QL
else:
STL = u_ - c0_star(p_, PL, MPL)
if (S < STL):
ret[i] = Wfan(S, PL, MPL, c0L)
else:
r_ = r_star_fan(p_, PL, MPL)
v_ = array([u_, 0, 0])
ret[i] = Cvec(r_, p_, v_, MPL)
else: # Left shock
SL = uL - Q(p_, PL, MPL) / ρL
if (S < SL):
ret[i] = QL
else:
r_ = r_star_shock(p_, PL, MPL)
v_ = array([u_, 0, 0])
ret[i] = Cvec(r_, p_, v_, MPL)
ret[i, -1] = -1
else:
if (p_ < pR): # Right fan
if (uR + c0R < S):
ret[i] = QR
else:
STR = u_ + c0_star(p_, PR, MPR)
if (STR < S):
ret[i] = Wfan(S, PR, MPR, -c0R)
else:
r_ = r_star_fan(p_, PR, MPR)
v_ = array([u_, 0, 0])
ret[i] = Cvec(r_, p_, v_, MPR)
else: # Right shock
SR = uR + Q(p_, PR, MPR) / ρR
if (SR < S):
ret[i] = QR
else:
r_ = r_star_shock(p_, PR, MPR)
v_ = array([u_, 0, 0])
ret[i] = Cvec(r_, p_, v_, MPR)
ret[i, -1] = 1
return ret
def rod_impact():
""" N = 2
cfl = 0.8
SPLIT = True
FLUX = 0
LSET = 3
RIEMANN_STICK = false
RIEMANN_RELAXATION = true
STAR_TOL = 1e-8
PRIM_RECONSTRUCT = true
"""
Lx = 0.55
Ly = 0.18
nx = 2000
tf = 60e-6
nx = int(nx)
ny = int(nx * Ly / Lx)
dX = [Lx / nx, Ly / ny]
MPa = Air_SG_SI
MPm = Cu_GRP_SI2
MPe = NM_CC_SI
pm = 1e5
pe = 1e5
pa = 1e5
v1 = array([2000, 0, 0])
v = zeros(3)
A = eye(3)
MPs = [MPa, MPe, MPm, MPm]
dX = [Lx / nx, Ly / ny]
Qm1 = pad(Cvec(MPm.ρ0, pm, v1, MPm, A, λ=0), (0, 3), 'constant')
Qm2 = pad(Cvec(MPm.ρ0, pm, v, MPm, A, λ=0), (0, 3), 'constant')
Qe = pad(Cvec(MPe.ρ0, pe, v, MPe, A, λ=1), (0, 3), 'constant')
Qa = pad(Cvec(MPa.ρ0, pa, v, MPa, A, λ=0), (0, 3), 'constant')
u = zeros([nx, ny, 18])
for i in range(nx):
for j in range(ny):
x = (i + 0.5) * dX[0]
y = (j + 0.5) * dX[1]
# projectile
if x <= 0.06 and 0.04 <= y <= 0.14:
u[i, j] = Qm1
u[i, j, -3] = 1
u[i, j, -2] = 1
u[i, j, -1] = 1
# casing
elif ((0.06 <= x <= 0.08 or 0.53 <= x <= 0.55) and
0.02 <= y <= 0.16) or \
(0.08 <= x <= 0.53 and
(0.02 <= y <= 0.04 or 0.14 <= y <= 0.16)):
u[i, j] = Qm2
u[i, j, -3] = 1
u[i, j, -2] = 1
u[i, j, -1] = -1
# explosive
elif 0.08 <= x <= 0.53 and 0.04 <= y <= 0.14:
u[i, j] = Qe
u[i, j, -3] = 1
u[i, j, -2] = -1
u[i, j, -1] = -1
# air
else:
u[i, j] = Qa
u[i, j, -3] = -1
u[i, j, -2] = -1
u[i, j, -1] = -1
u = u[:, int(ny / 2):]
return u, MPs, tf, dX, 'halfy'
wL = array([QL for i in range(N)])
wR = array([QR for i in range(N)])
"""
wL = zeros([N, NV])
wR = zeros([N, NV])
v0 = zeros(3)
J0 = zeros(3)
for i in range(N):
ρL = 3 - NODES[i]
pL = ρL
AL = ρL**(1 / 3) * eye(3)
ρR = 2 - NODES[i]
pR = ρR
AR = ρR**(1 / 3) * eye(3)
wL[i] = Cvec(ρL, pL, v0, AL, J0, MP)
wR[i] = Cvec(ρR, pR, v0, AR, J0, MP)
WwL = dot(W, wL)
WwR = dot(W, wR)
qL0 = array([wL for i in range(N)])
qR0 = array([wR for i in range(N)])
nX = NT * NV
x0 = zeros(2 * nX + 6 * N)
x0[0:nX] = qL0.ravel()
x0[nX:2 * nX] = qR0.ravel()
dt = 0.01
def f(x):
def confined_explosive():
""" N = 2
cfl = 0.8
SPLIT = True
FLUX = 1
LSET = 3 / 4
RIEMANN_STICK = false
RIEMANN_RELAXATION = true
STAR_TOL = 1e-8
PRIM_RECONSTRUCT = true
"""
BACK_PLATE = False
AIR_GAP = False
NITRO = False
Lx = 0.051
Ly = 0.09
nx = 200
tf = 4.9e-6
o = 0.0015 if AIR_GAP else 0
ny = int(nx * Ly / Lx)
dX = [Lx / nx, Ly / ny]
MPm = Steel_SMGP_SI
MPa = Air_SG_SI
if NITRO:
MPe = NM_CC_SI
else:
MPe = C4_JWL_SI
pm = 1e5
pe = 1e5
pa = 1e5
v1 = array([700, 0, 0])
v = zeros(3)
A = eye(3)
if AIR_GAP:
MPs = [MPa, MPe, MPm, MPm, VAC]
u = zeros([nx, ny, 19])
u[:, :, -4:] = 1
else:
MPs = [MPe, MPm, MPm, VAC]
u = zeros([nx, ny, 18])
u[:, :, -3:] = 1
dX = [Lx / nx, Ly / ny]
Qm1 = Cvec(MPm.ρ0, pm, v1, MPm, A, λ=0)
Qm2 = Cvec(MPm.ρ0, pm, v, MPm, A, λ=0)
Qe = Cvec(MPe.ρ0, pe, v, MPe, A, λ=1)
Qa = Cvec(MPa.ρ0, pa, v, MPa, A, λ=0)
for i in range(nx):
for j in range(ny):
x = (i + 0.5) * dX[0]
y = (j + 0.5) * dX[1]
# air gap
if 0.033 <= x <= 0.033 + o:
u[i, j, :15] = Qa
u[i, j, -4:] = -1
# projectile
elif x <= 0.03 and 0.036 <= y <= 0.054:
u[i, j, :15] = Qm1
u[i, j, -1] = -1
# front plate
elif 0.03 <= x <= 0.033:
u[i, j, :15] = Qm2
u[i, j, -2:] = -1
# explosive
elif 0.033 + o <= x <= 0.039 + o:
u[i, j, :15] = Qe
u[i, j, -3:] = -1
# back plate
elif 0.039 + o <= x:
if BACK_PLATE:
u[i, j, :15] = Qm2
u[i, j, -2:] = -1
else:
u[i, j, :15] = Qe
u[i, j, -3:] = -1
#u = u[:, int(ny/2):]
return u, MPs, tf, dX, 'transitive'