def riemann_constraints(Q, sgn, MP):
M = M_prim(Q, 0, MP)
λ, L = eig(M, left=True, right=False)
λ = λ.real
L = L.T
Lhat = L[λ.argsort()]
Lhat[:n1] *= 0
P = State(Q, MP)
σρ = P.dσdρ()
σA = P.dσdA()
Lhat[:3, 0] = -σρ[0]
Lhat[0, 1] = 1
for i in range(3):
Lhat[:3, 5 + 3 * i:8 + 3 * i] = -σA[0, :, i]
if THERMAL:
Lhat[3, 0] = P.dTdρ()
Lhat[3, 1] = P.dTdp()
Lhat[-n1:, 2:5] *= -sgn
if THERMAL:
Lhat[-n1:, 14] *= -sgn
return Lhat
def M_prim(Q, d, MP):
""" The system jacobian of the primitive system
NOTE: Uses typical ordering
"""
P = State(Q, MP)
ρ = P.ρ
p = P.p()
A = P.A
v = P.v
c0 = c_0(ρ, p, A, MP)
ret = v[d] * eye(NV)
ret[0, 2 + d] = ρ
ret[1, 2 + d] = ρ * c0**2
ret[2 + d, 1] = 1 / ρ
if VISCOUS:
σ = P.σ()
dσdρ = P.dσdρ()
dσdA = P.dσdA()
ret[1, 2:5] += σ[d] - ρ * dσdρ[d]
ret[2:5, 0] = -1 / ρ * dσdρ[d]
ret[2:5, 5:14] = -1 / ρ * dσdA[d].reshape([3, 9])
ret[5 + d, 2:5] = A[0]
ret[8 + d, 2:5] = A[1]
ret[11 + d, 2:5] = A[2]
if THERMAL:
dTdρ = P.dTdρ()
dTdp = P.dTdp()
T = P.T()
ch = c_h(ρ, T, MP)
ret[1, 14 + d] = ρ * ch**2 / dTdp
ret[14 + d, 0] = dTdρ / ρ
ret[14 + d, 1] = dTdp / ρ
return ret