def quasilinear_eigenvectors_left(self, q, x, t):
# TODO: needs to be implemented
errors.MissingImplementation(self.class_str, "quasilinear_eigenvectors_left")
g = self.gravity_constant
p = swme.get_primitive_variables(q)
h = p[0]
u = p[1]
eigenvectors = np.zeros((self.num_moments + 2, self.num_moments + 2))
if self.num_moments == 0:
sqrt_gh = np.sqrt(g * h)
eigenvectors[0, 0] = 0.5 * (u + sqrt_gh) / sqrt_gh
eigenvectors[0, 1] = -0.5 / sqrt_gh
eigenvectors[1, 0] = -0.5 * (u - sqrt_gh) / sqrt_gh
eigenvectors[1, 1] = 0.5 / sqrt_gh
elif self.num_moments == 1:
s = p[2]
ghs2 = g * h + s * s
sqrt_gh_s2 = np.sqrt(ghs2)
eigenvectors[0, 0] = (
1.0 / 6.0 * (3.0 * g * h - s * s + 3.0 * sqrt_gh_s2 * u) / ghs2
)
eigenvectors[0, 1] = -0.5 / sqrt_gh_s2
eigenvectors[0, 2] = 1.0 / 3.0 * s / ghs2
eigenvectors[1, 0] = 4.0 / 3.0 * s * s / ghs2
eigenvectors[1, 1] = 0.0
eigenvectors[1, 2] = -2.0 / 3.0 * s / ghs2
eigenvectors[2, 0] = (
-1.0
/ 6.0
* (3.0 * ghs2 * u - (3.0 * g * h - s * s) * sqrt_gh_s2)
/ np.power(ghs2, 1.5)
)
eigenvectors[2, 1] = 0.5 / sqrt_gh_s2
eigenvectors[2, 2] = 1.0 / 3.0 * s / ghs2
elif self.num_moments == 2:
raise errors.NotImplementedParameter(
"ShallowWaterLinearizedMomentEquations.quasilinear_eigenvectors_left",
"num_moments",
2,
)
elif self.num_moments == 3:
raise errors.NotImplementedParameter(
"ShallowWaterLinearizedMomentEquations.quasilinear_eigenvectors_left",
"num_moments",
3,
)
return eigenvectors
def roe_averaged_states(self, left_state, right_state, x, t):
errors.MissingImplementation(self.class_str, "roe_averaged_states")
p_left = swme.get_primitive_variables(left_state)
p_right = swme.get_primitive_variables(right_state)
# roe averaged primitive variables
p_avg = np.zeros(p_left.shape)
# h_avg
p_avg[0] = 0.5 * (p_left[0] + p_right[0])
d = np.sqrt(p_left[0]) + np.sqrt(p_right[0])
for i in range(1, self.num_moments + 2):
# u_avg, s_avg, k_avg, m_avg
p_avg[i] = (np.sqrt(p_left[0]) * p_left[i] +
np.sqrt(p_right[0]) * p_right[i]) / d
# transform back to conserved variables
return swme.get_conserved_variables(p_avg)
def quasilinear_eigenvectors_right(self, q, x, t):
# TODO: needs to be implemented
errors.MissingImplementation(self.class_str, "quasilinear_eigenvectors_right")
g = self.gravity_constant
p = swme.get_primitive_variables(q)
h = p[0]
u = p[1]
eigenvectors = np.zeros((self.num_moments + 2, self.num_moments + 2))
if self.num_moments == 0:
sqrt_gh = np.sqrt(g * h)
eigenvectors[0, 0] = 1.0
eigenvectors[1, 0] = u - sqrt_gh
eigenvectors[0, 1] = 1.0
eigenvectors[1, 1] = u + sqrt_gh
elif self.num_moments == 1:
s = p[2]
sqrt_gh_s2 = np.sqrt(g * h + s * s)
eigenvectors[0, 0] = 1.0
eigenvectors[1, 0] = u - sqrt_gh_s2
eigenvectors[2, 0] = 2.0 * s
eigenvectors[0, 1] = 1.0
eigenvectors[1, 1] = u
eigenvectors[2, 1] = -0.5 * (3.0 * g * h - s * s) / s
eigenvectors[0, 2] = 1.0
eigenvectors[1, 2] = u + sqrt_gh_s2
eigenvectors[2, 2] = 2.0 * s
elif self.num_moments == 2:
raise errors.NotImplementedParameter(
"ShallowWaterLinearizedMomentEquations.quasilinear_eigenvalues_right",
"num_moments",
2,
)
elif self.num_moments == 3:
raise errors.NotImplementedParameter(
"ShallowWaterLinearizedMomentEquations.quasilinear_eigenvectors_right",
"num_moments",
3,
)
return eigenvectors
def do_q_jacobian_eigenvectors(self, q):
# Flux Jacobian Eigenvectors are very complex for even 1 moment
# Code should need eigenvectors of quasilinear matrix instead
errors.MissingImplementation(self.class_str, "do_q_jacobian_eigenvectors")
def roe_averaged_states(self, left_state, right_state, x, t):
raise errors.MissingImplementation("ShallowWaterMomentEquations2D",
"roe_averaged_states")
def mesh_norm(self, elem_slice=None, ord=None):
# norm of coefficients including element volume
raise errors.MissingImplementation("DGSolution", "mesh_norm")
def quasilinear_eigenvectors_left(self, q, x, t, n):
# TODO: needs to be implemented
errors.MissingImplementation(self.class_str,
"quasilinear_eigenvectors_left")