def test_shallow_water_gc():
import ibvp.sym as sym
dim = 2
col_height = sym.Field("eta")
# "mom"entum really is column height * velocity
mom = sym.MultiVectorField("mom")
d1 = sym.Derivative()
d2 = sym.Derivative()
d3 = sym.Derivative()
eqns = sym.join(
sym.d_dt(col_height)
+ (d1.nabla | d1(mom)),
sym.d_dt(mom)
+ d2(mom * (mom | d2.nabla)/col_height)
+ 0.5*d3.nabla*d3(col_height**2)
)
print(sym.pretty(eqns))
from ibvp.language import PDESystem
system = PDESystem(
ambient_dim=dim,
pde_system=eqns,
unknowns=[col_height, mom],
)
from ibvp.target.proteus import generate_proteus_problem_file
generate_proteus_problem_file(system, "ShallowWater")
def test_very_nonlinear_burgers():
ambient_dim = 2
p = 1
q = 2
r = 2
u = sym.Field("u")
B = np.array([1.0, 2.0])
Adiff = 0.001
C = 0.0001
eqns = sym.join(
sym.d_dt(u**p)
+ sym.div(B * u**q)
- sym.div(Adiff * sym.grad(u**r))
+ C * u
)
print(sym.pretty(eqns))
print(generate_proteus_problem_file(
PDESystem(
ambient_dim=ambient_dim,
pde_system=eqns,
unknowns=[u],
),
"Burgers"))
def test_advection():
u = sym.Field("u")
eqns = sym.join(sym.d_dt(u) + sym.d_dx(u))
print(sym.pretty(eqns))
print(generate_proteus_problem_file(
PDESystem(
ambient_dim=1,
pde_system=eqns,
unknowns=[u],
),
"Advection"))
def test_heat():
ambient_dim = 2
u = sym.Field("u")
eqns = sym.join(
sym.d_dt(u)
- sym.div(sym.grad(u))
)
print(sym.pretty(eqns))
generate_proteus_problem_file(
PDESystem(
ambient_dim=ambient_dim,
pde_system=eqns,
unknowns=[u],
),
"Heat")
def test_parabolic_system():
ambient_dim = 2
u = sym.Field("u")
v = sym.Field("v")
eqns = sym.join(
sym.d_dt(u) - sym.div(sym.grad(u-v)),
sym.d_dt(v) - sym.div(sym.grad(u+v)),
)
print(sym.pretty(eqns))
generate_proteus_problem_file(
PDESystem(
ambient_dim=ambient_dim,
pde_system=eqns,
unknowns=[u, v],
),
"ParabolicSystem")
def test_burgers():
ambient_dim = 2
u = sym.Field("u")
vec = np.array([1.0, 2.0])
eqns = sym.join(
sym.d_dt(u)
+ sym.div(vec * u**2)
- sym.div(sym.grad(u))
)
print(sym.pretty(eqns))
generate_proteus_problem_file(
PDESystem(
ambient_dim=ambient_dim,
pde_system=eqns,
unknowns=[u],
),
"Burgers")
def test_wave():
dim = 3
u = sym.Field("u")
f = sym.Field("f")
c = sym.Parameter("c")
v = sym.VectorField("v")
eqns = sym.join(
sym.d_dt(u)
+ c * sym.div(v) - f,
sym.d_dt(v)
+ c * sym.grad(u)
)
print(sym.pretty(eqns))
generate_proteus_problem_file(
PDESystem(
ambient_dim=dim,
pde_system=eqns,
unknowns=[u, v],
),
"Wave")