def viscous_shock_ns():
""" 10.1016/j.jcp.2016.02.015
4.13 Viscous shock profile
"""
tf = 0.2
nx = 200
x = arange(-0.5, 0.5, 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])
v -= v[0] # Velocity in shock 0
u = zeros([nx, 5])
for i in range(nx):
u[i] = make_Q(ρ[i], p[i], array([v[i], 0, 0]))
L = [1.]
ret = pde_solver(u, tf, L, F=F_navier_stokes, cfl=0.6)
plt.plot(ret[-1, :, 2] / ret[-1, :, 0])
plt.show()
return ret
def viscous_shock_gpr():
""" 10.1016/j.jcp.2016.02.015
4.13 Viscous shock profile
"""
tf = 0.2
nx = 200
x = arange(-0.5, 0.5, 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])
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]), A, J)
L = [1.]
ret = pde_solver(u, tf, L, F=F_gpr, B=B_gpr, S=S_gpr, cfl=0.6)
plt.plot(ret[-1, :, 2] / ret[-1, :, 0])
plt.show()
return ret
def detonation_wave():
nx = 400
ρL = 1.4
pL = 1
vL = [0, 0, 0]
λL = 0
EL = energy(ρL, pL, vL, λL)
ρR = 0.887565
pR = 0.191709
vR = [-0.57735, 0, 0]
λR = 1
ER = energy(ρR, pR, vR, λR)
QL = ρL * array([1, EL] + vL + [λL])
QR = ρR * array([1, ER] + vR + [λR])
u = zeros([nx, 6])
for i in range(nx):
if i / nx < 0.25:
u[i] = QL
else:
u[i] = QR
tf = 0.5
L = [1.]
ret = pde_solver(u,
tf,
L,
F=F_reactive_euler,
S=S_reactive_euler,
stiff=False,
cfl=0.6,
flux='roe',
order=3)
plt.plot(ret[-1, :, 0])
plt.show()
return ret
def taylor_green_vortex_2d():
""" 10.1016/j.jcp.2016.02.015
4.10 2D Taylor-Green Vortex
"""
L = [2 * pi, 2 * pi]
nx = 50
ny = 50
tf = 1
C = 100 / γ
ρ = 1
v = zeros(3)
u = zeros([nx, ny, 5])
for i in range(nx):
for j in range(ny):
x = (i + 0.5) * L[0] / nx
y = (j + 0.5) * L[1] / ny
v[0] = sin(x) * cos(y)
v[1] = -cos(x) * sin(y)
p = C + (cos(2 * x) + cos(2 * y)) / 4
u[i, j] = make_Q(ρ, p, v)
ret = pde_solver(u,
tf,
L,
F=F_navier_stokes,
cfl=0.9,
order=2,
boundaryTypes='periodic')
x = linspace(0, L[0], nx)
y = linspace(0, L[1], ny)
ut = ret[-1, :, :, 2] / ret[-1, :, :, 0]
vt = ret[-1, :, :, 3] / ret[-1, :, :, 0]
plt.streamplot(x, y, ut, vt)
plt.show()
return ret
def sod_shock():
nx = 200
ny = 5
ρL = 1
pL = 1
vL = 0
ρR = 0.125
pR = 0.1
vR = 0
QL = ρL * array([1., energy(ρL, pL, vL), vL])
QR = ρR * array([1., energy(ρR, pR, vR), vR])
u_ = zeros([nx, 3])
for i in range(nx):
if i / nx < 0.5:
u_[i] = QL
else:
u_[i] = QR
tf = 0.2
u = zeros([nx, ny, 3])
for i in range(ny):
u[:, i] = u_
L = [1., .2]
boundaryTypes = ['transitive', 'periodic']
ret = pde_solver(u,
tf,
L,
F=F_euler,
stiff=False,
boundaryTypes=boundaryTypes)
plot_2d(L, ret[-1, :, :, 0])
return ret