def do_q_jacobian_eigenvectors(self, q):
g = self.gravity_constant
p = get_primitive_variables(q)
h = p[0]
u = p[1]
if self.num_moments == 0:
eigenvectors = np.array([[1, u - np.sqrt(g * h)],
[1, u + np.sqrt(g * h)]])
elif self.num_moments == 1:
s = p[2]
eigenvectors = np.array([
[1, u - np.sqrt(g * h + s * s), 2 * s],
[1, u, -1 / 2 * (3 * g * h - s * s) / s],
[1, u + np.sqrt(g * h + s * s), 2 * s],
])
elif self.num_moments == 2:
raise errors.NotImplementedParameter(
"FluxFunction.do_q_jacobian_eigenvectors",
"num_moments",
self.num_moments,
)
elif self.num_moments == 3:
raise errors.NotImplementedParameter(
"FluxFunction.do_q_jacobian_eigenvectors",
"num_moments",
self.num_moments,
)
return eigenvectors
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 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 quasilinear_eigenvectors_right(self, q, x, t, n):
g = self.gravity_constant
p = 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:
sqrtgh = np.sqrt(g * h)
eigenvectors[0, 0] = 1.0
eigenvectors[1, 0] = u - sqrtgh
eigenvectors[0, 1] = 1.0
eigenvectors[1, 1] = u + sqrtgh
elif self.num_moments == 1:
s = p[2]
sqrtghs2 = np.sqrt(g * h + s * s)
eigenvectors[0, 0] = 1.0
eigenvectors[1, 0] = u - sqrtghs2
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 + sqrtghs2
eigenvectors[2, 2] = 2.0 * s
elif self.num_moments == 2:
raise errors.NotImplementedParameter(
"ShallowWaterMomentEquations.quasilinear_eigenvalues_right",
"num_moments",
2,
)
elif self.num_moments == 3:
raise errors.NotImplementedParameter(
"ShallowWaterMomentEquations.quasilinear_eigenvectors_right",
"num_moments",
3,
)
return eigenvectors
def gauss_pts_and_wgts_2d_triangle_canonical(quad_order=5):
# quadrature on canonical triangle
canonical_volume = canonical_element.Triangle.volume
if quad_order == 1:
degree_of_exactness = 1
elif quad_order == 2:
degree_of_exactness = 2
elif quad_order == 3:
degree_of_exactness = 4
elif quad_order == 4:
degree_of_exactness = 6
elif quad_order == 5:
degree_of_exactness = 8
else:
raise errors.NotImplementedParameter(
"gauss_pts_and_wgts_2d_triangle_canonical", "quad_order", quad_order
)
if degree_of_exactness == 1:
quad_wgts = canonical_volume * np.array([1.0])
quad_pts_barycentric = np.array([[1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0]])
elif degree_of_exactness == 2:
w0 = 1.0 / 3.0
quad_wgts = canonical_volume * np.array([w0, w0, w0])
p0 = np.array([2.0 / 3.0, 1.0 / 6.0, 1.0 / 6.0])
quad_pts_barycentric = np.array([p0, np.roll(p0, 1), np.roll(p0, 2)])
elif degree_of_exactness == 3:
w0 = -0.5625
w1 = 25.0 / 48.0
quad_wgts = canonical_volume * np.array([w0, w1, w1, w1])
p0 = np.array([1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0])
p1 = np.array([0.6, 0.2, 0.2])
quad_pts_barycentric = np.array([p0, p1, np.roll(p1, 1), np.roll(p1, 2)])
elif degree_of_exactness == 4:
w0 = 0.223381589678011
w1 = 0.109951743655322
quad_wgts = canonical_volume * np.array([w0, w0, w0, w1, w1, w1])
p0 = np.array([0.108103018168070, 0.445948490915965, 0.445948490915965])
p1 = np.array([0.816847572980459, 0.091576213509771, 0.091576213509771])
quad_pts_barycentric = np.array(
[p0, np.roll(p0, 1), np.roll(p0, 2), p1, np.roll(p1, 1), np.roll(p1, 2)]
)
elif degree_of_exactness == 5:
w0 = 0.225
w1 = 0.132394152788506
w2 = 0.125939180544827
quad_wgts = canonical_volume * np.array([w0, w1, w1, w1, w2, w2, w2])
p0 = np.array([1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0])
p1 = np.array([0.059715871789770, 0.470142064105115, 0.470142064105115])
p2 = np.array([0.797426985353087, 0.101286507323456, 0.101286507323456])
quad_pts_barycentric = np.array(
[p0, p1, np.roll(p1, 1), np.roll(p1, 2), p2, np.roll(p2, 1), np.roll(p2, 2)]
)
elif degree_of_exactness == 6:
w0 = 0.116786275726379
w1 = 0.050844906370207
w2 = 0.082851075618374
quad_wgts = canonical_volume * np.array(
[w0, w0, w0, w1, w1, w1, w2, w2, w2, w2, w2, w2]
)
p0 = np.array([0.501426509658179, 0.249286745170910, 0.249286745170910])
p1 = np.array([0.873821971016996, 0.063089014491502, 0.063089014491502])
p2 = np.array([0.053145049844817, 0.310352451033784, 0.636502499121399])
p3 = np.flip(p2)
quad_pts_barycentric = np.array(
[
p0,
np.roll(p0, 1),
np.roll(p0, 2),
p1,
np.roll(p1, 1),
np.roll(p1, 2),
p2,
np.roll(p2, 1),
np.roll(p2, 2),
p3,
np.roll(p3, 1),
np.roll(p3, 2),
]
)
elif degree_of_exactness == 8:
w0 = 0.144315607677787
w1 = 0.095091634267285
w2 = 0.103217370534718
w3 = 0.032458497623198
w4 = 0.027230314174435
quad_wgts = canonical_volume * np.array(
[w0, w1, w1, w1, w2, w2, w2, w3, w3, w3, w4, w4, w4, w4, w4, w4]
)
p0 = np.array([1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0])
p1 = np.array([0.081414823414554, 0.459292588292723, 0.459292588292723])
p2 = np.array([0.658861384496480, 0.170569307751760, 0.170569307751760])
p3 = np.array([0.898905543365938, 0.050547228317031, 0.050547228317031])
p4 = np.array([0.008394777409958, 0.263112829634638, 0.728492392955404])
p5 = np.flip(p4)
quad_pts_barycentric = np.array(
[
p0,
p1,
np.roll(p1, 1),
np.roll(p1, 2),
p2,
np.roll(p2, 1),
np.roll(p2, 2),
p3,
np.roll(p3, 1),
np.roll(p3, 2),
p4,
np.roll(p4, 1),
np.roll(p4, 2),
p5,
np.roll(p5, 1),
np.roll(p5, 2),
]
)
else:
raise errors.NotImplementedParameter(
"gauss_pts_and_wgts_2d_triangle_canonical",
"degree_of_exactness",
degree_of_exactness,
)
vertices = canonical_element.Triangle.vertices
quad_pts = (quad_pts_barycentric @ vertices).T
return (quad_pts, quad_wgts)