def main(argv=None):
options = parse_args(argv=argv)
# vvvvvvvvvvvvvvvv #
approx_order = 2
# ^^^^^^^^^^^^^^^^ #
# Setup output names
outputs_folder = options.output_dir
domain_name = "domain_1D"
problem_name = "iburgers_1D"
output_folder = pjoin(outputs_folder, problem_name, str(approx_order))
output_format = "vtk"
save_timestn = 100
clear_folder(pjoin(output_folder, "*." + output_format))
configure_output({
'output_screen':
True,
'output_log_name':
pjoin(output_folder, f"last_run_{problem_name}_{approx_order}.txt")
})
# ------------
# | Get mesh |
# ------------
X1 = 0.
XN = 1.
n_nod = 100
n_el = n_nod - 1
mesh = get_gen_1D_mesh_hook(X1, XN, n_nod).read(None)
# -----------------------------
# | Create problem components |
# -----------------------------
integral = Integral('i', order=approx_order * 2)
domain = FEDomain(domain_name, mesh)
omega = domain.create_region('Omega', 'all')
left = domain.create_region('Gamma1', 'vertices in x == %.10f' % X1,
'vertex')
right = domain.create_region('Gamma2', 'vertices in x == %.10f' % XN,
'vertex')
field = DGField('dgfu',
nm.float64,
'scalar',
omega,
approx_order=approx_order)
u = FieldVariable('u', 'unknown', field, history=1)
v = FieldVariable('v', 'test', field, primary_var_name='u')
MassT = Term.new('dw_dot(v, u)', integral, omega, u=u, v=v)
velo = nm.array(1.0)
def adv_fun(u):
vu = velo.T * u[..., None]
return vu
def adv_fun_d(u):
v1 = velo.T * nm.ones(u.shape + (1, ))
return v1
burg_velo = velo.T / nm.linalg.norm(velo)
def burg_fun(u):
vu = burg_velo * u[..., None]**2
return vu
def burg_fun_d(u):
v1 = 2 * burg_velo * u[..., None]
return v1
StiffT = Term.new('dw_ns_dot_grad_s(fun, fun_d, u[-1], v)',
integral,
omega,
u=u,
v=v,
fun=burg_fun,
fun_d=burg_fun_d)
# alpha = Material('alpha', val=[.0])
# FluxT = AdvectDGFluxTerm("adv_lf_flux(a.val, v, u)", "a.val, v, u[-1]",
# integral, omega, u=u, v=v, a=a, alpha=alpha)
FluxT = Term.new('dw_dg_nonlinear_laxfrie_flux(fun, fun_d, v, u[-1])',
integral,
omega,
u=u,
v=v,
fun=burg_fun,
fun_d=burg_fun_d)
eq = Equation('balance', MassT - StiffT + FluxT)
eqs = Equations([eq])
# ------------------------------
# | Create boundary conditions |
# ------------------------------
left_fix_u = EssentialBC('left_fix_u', left, {'u.all': 1.0})
right_fix_u = EssentialBC('right_fix_u', right, {'u.all': 0.0})
# ----------------------------
# | Create initial condition |
# ----------------------------
def ghump(x):
"""
Nice gaussian.
"""
return nm.exp(-200 * x**2)
def ic_wrap(x, ic=None):
return ghump(x - .3)
ic_fun = Function('ic_fun', ic_wrap)
ics = InitialCondition('ic', omega, {'u.0': ic_fun})
# ------------------
# | Create problem |
# ------------------
pb = Problem(problem_name,
equations=eqs,
conf=Struct(options={"save_times": save_timestn},
ics={},
ebcs={},
epbcs={},
lcbcs={},
materials={}),
active_only=False)
pb.setup_output(output_dir=output_folder, output_format=output_format)
pb.set_ics(Conditions([ics]))
# ------------------
# | Create limiter |
# ------------------
limiter = MomentLimiter1D
# ---------------------------
# | Set time discretization |
# ---------------------------
CFL = .2
max_velo = nm.max(nm.abs(velo))
t0 = 0
t1 = .2
dx = nm.min(mesh.cmesh.get_volumes(1))
dt = dx / max_velo * CFL / (2 * approx_order + 1)
tn = int(nm.ceil((t1 - t0) / dt))
dtdx = dt / dx
# ------------------
# | Create solver |
# ------------------
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'is_linear': True}, lin_solver=ls, status=nls_status)
tss_conf = {
't0': t0,
't1': t1,
'n_step': tn,
'limiters': {
"dgfu": limiter
}
}
tss = TVDRK3StepSolver(tss_conf, nls=nls, context=pb, verbose=True)
# ---------
# | Solve |
# ---------
pb.set_solver(tss)
state_end = pb.solve()
output("Solved equation \n\n\t\t u_t - div(f(u))) = 0\n")
output(f"With IC: {ic_fun.name}")
# output("and EBCs: {}".format(pb.ebcs.names))
# output("and EPBCS: {}".format(pb.epbcs.names))
output("-------------------------------------")
output(f"Approximation order is {approx_order}")
output(f"Space divided into {mesh.n_el} cells, " +
f"{len(mesh.coors)} steps, step size is {dx}")
output(f"Time divided into {tn - 1} nodes, {tn} steps, step size is {dt}")
output(f"CFL coefficient was {CFL} and " +
f"order correction {1 / (2 * approx_order + 1)}")
output(f"Courant number c = max(abs(u)) * dt/dx = {max_velo * dtdx}")
output("------------------------------------------")
output(f"Time stepping solver is {tss.name}")
output(f"Limiter used: {limiter.name}")
output("======================================")
# ----------
# | Plot 1D|
# ----------
if options.plot:
load_and_plot_fun(output_folder, domain_name, t0, t1,
min(tn, save_timestn), ic_fun)
ic_fun = Function('ic_fun', ic_wrap)
ics = InitialCondition('ic', omega, {'u.0': ic_fun})
# ------------------
# | Create problem |
# ------------------
pb = Problem(problem_name,
equations=eqs,
conf=Struct(options={"save_times": save_timestn},
ics={},
ebcs={},
epbcs={},
lcbcs={},
materials={}),
active_only=False)
pb.setup_output(output_dir=output_folder, output_format=output_format)
pb.set_ics(Conditions([ics]))
# ------------------
# | Create limiter |
# ------------------
limiter = MomentLimiter1D
# ---------------------------
# | Set time discretization |
# ---------------------------
CFL = .2
max_velo = nm.max(nm.abs(velo))
t0 = 0
t1 = .2
dx = nm.min(mesh.cmesh.get_volumes(1))