def check_star_convergence(QL_, QR_, MPL, MPR):
PL_ = State(QL_, MPL)
if MPR.EOS > -1: # not a vacuum
PR_ = State(QR_, MPR)
ρ0 = min(MPL.ρ0, MPR.ρ0)
b02 = min(MPL.b02, MPR.b02)
cond = amax(abs(PL_.Σ()[0] - PR_.Σ()[0])) / (b02 * ρ0) < STAR_TOL
cond &= abs(PL_.v[0] - PR_.v[0]) / sqrt(b02) < STAR_TOL
else:
ρ0 = MPL.ρ0
b02 = MPL.b02
cond = amax(abs(PL_.Σ()[0])) / (b02 * ρ0) < STAR_TOL
if THERMAL:
if MPR.EOS > -1:
q0 = min(q_dims(MPL), q_dims(MPR))
T0 = min(MPL.T0, MPR.T0)
cond &= abs(PL_.q()[0] - PR_.q()[0]) / q0 < STAR_TOL
cond &= abs(PL_.T() - PR_.T()) / T0 < STAR_TOL
else:
q0 = q_dims(MPL)
cond &= abs(PL_.q()[0]) / q0 < STAR_TOL
return cond
def star_stepper_obj(x, QL, QR, dt, MPL, MPR):
X = x.reshape([2, 21])
ret = zeros([2, 21])
QL_ = X[0, :17]
QR_ = X[1, :17]
PL = State(QL, MPL)
PR = State(QR, MPR)
PL_ = State(QL_, MPL)
PR_ = State(QR_, MPR)
pL = Cvec_to_Pvec(QL, MPL)
pR = Cvec_to_Pvec(QR, MPR)
pL_ = Cvec_to_Pvec(QL_, MPL)
pR_ = Cvec_to_Pvec(QR_, MPR)
ML = riemann_constraints2(PL, 'L', MPL)[:17, :17]
MR = riemann_constraints2(PR, 'R', MPR)[:17, :17]
xL_ = X[0, 17:]
xR_ = X[1, 17:]
xL = zeros(4)
xR = zeros(4)
xL[:3] = PL.Σ()[0]
xR[:3] = PR.Σ()[0]
xL[3] = PL.q()[0]
xR[3] = PR.q()[0]
ret[0, :4] = dot(ML[:4], pL_ - pL) - (xL_ - xL)
ret[1, :4] = dot(MR[:4], pR_ - pR) - (xR_ - xR)
SL = source_prim(QL, MPL)[:17]
SR = source_prim(QR, MPR)[:17]
SL_ = source_prim(QL_, MPL)[:17]
SR_ = source_prim(QR_, MPR)[:17]
ret[0, 4:17] = dot(ML[4:], (pL_ - pL) - dt / 2 * (SL + SL_))
ret[1, 4:17] = dot(MR[4:], (pR_ - pR) - dt / 2 * (SR + SR_))
bR = zeros(4)
bL = zeros(4)
bL[:3] = PL_.v
bR[:3] = PR_.v
bL[3] = PL_.T()
bR[3] = PR_.T()
ret[0, 17:] = xL_ - xR_
ret[1, 17:] = bL - bR
return ret.ravel()
def star_states_stiff(QL, QR, dt, MPL, MPR):
PL = State(QL, MPL)
PR = State(QR, MPR)
x0 = zeros(42)
x0[:21] = concatenate([QL, PL.Σ()[0], [PL.q()[0]]])
x0[21:] = concatenate([QR, PR.Σ()[0], [PR.q()[0]]])
def obj(x):
return star_stepper_obj(x, QL, QR, dt, MPL, MPR)
ret = newton_krylov(obj, x0).reshape([2, 21])
return ret[0, :17], ret[1, :17]
def F_cons(Q, d, MP):
ret = zeros(NV)
P = State(Q, MP)
ρ = P.ρ
p = P.p()
E = P.E
v = P.v
vd = v[d]
ρvd = ρ * vd
ret[0] = ρvd
ret[1] = ρvd * E + p * vd
ret[2:5] = ρvd * v
ret[2 + d] += p
if VISCOUS:
A = P.A
σ = P.σ()
σd = σ[d]
ret[1] -= dot(σd, v)
ret[2:5] -= σd
Av = dot(A, v)
ret[5 + d] = Av[0]
ret[8 + d] = Av[1]
ret[11 + d] = Av[2]
if THERMAL:
J = P.J
T = P.T()
q = P.q()
ret[1] += q[d]
ret[14:17] = ρvd * J
ret[14 + d] += T
if MULTI:
λ = P.λ
ret[17] = ρvd * λ
return ret