def get_weno_grid(self, dx, dt, T):
left_boundary = self.x_low - dx * 0.5
right_boundary = self.x_high + dx * 0.5
ncells = int((self.x_high - self.x_low) / dx + 1.) # need to be very small
num_t = int(T/dt + 1.)
w = Weno3(left_boundary, right_boundary, ncells, self.flux, self.flux_deriv, self.max_flux_deriv,
dx = dx, dt = dt, num_t = num_t + 100)
x_center = w.get_x_center()
u0 = self.init_condition(x_center, self.args.initial_t)
w.integrate(u0, T)
solutions = w.u_grid[:num_t,:]
return solutions
def get_weno_grid(init_condition,
dx=0.02,
dt=0.004,
T=0.8,
x_low=-1,
x_high=1,
boundary='periodic',
eta=0,
forcing=None,
ncells=None,
num_t=None,
flux_name='u2'):
"""
dx: grid size. e.g. 0.02
dt: time step size. e.g. 0.004
T: evolve time. e.g. 1
x_low: if the grid is in the range [-1,1], then x_low = -1.
x_high: if the grid is in the range [-1,1], then x_low = 1.
init_condition: a function that computes the initial values of u. e.g. the init func above.
return: a grid of size num_t x num_x
where num_t = T/dt + 1
num_x = (x_high - x_low) / dx + 1
"""
left_boundary = x_low - dx * 0.5
right_boundary = x_high + dx * 0.5
if ncells is None:
ncells = int((x_high - x_low) / dx + 1.) # need to be very small
if num_t is None:
num_t = int(T / dt + 1.)
w = Weno3(left_boundary,
right_boundary,
ncells,
lambda x: flux(val=x, flux=flux_name),
lambda x: flux_deriv(val=x, flux=flux_name),
lambda a, b: max_flux_deriv(a=a, b=b, flux=flux_name),
dx=dx,
dt=dt,
num_t=num_t + 100,
boundary=boundary,
eta=eta,
forcing=forcing)
x_center = w.get_x_center()
u0 = init_condition(x_center)
w.integrate(u0, T, num_t=num_t)
solutions = w.u_grid[:num_t, :]
return solutions
def evolve(x_center, t, u0):
dx = x_center[1] - x_center[0]
cfl = 0.2
left_boundary = x_center[0] - dx * 0.5
right_boundary = x_center[-1] + dx * 0.5
ncells = len(x_center)
w = Weno3(left_boundary,
right_boundary,
ncells,
flux,
flux_deriv,
max_flux_deriv,
dx=dx,
dt=dx * cfl,
cfl_number=cfl,
record=False)
return w.integrate(u0, t)
def evolve(x_center, u0, t, animation=0):
dx = x_center[1] - x_center[0]
cfl = 0.2
left_boundary = x_center[0] - dx * 0.5
right_boundary = x_center[-1] + dx * 0.5
ncells = len(x_center)
dt = dx * cfl
evolve_num = int(t / dt)
w = Weno3(left_boundary,
right_boundary,
ncells,
flux,
flux_deriv,
max_flux_deriv,
dx=dx,
dt=dx * cfl,
cfl_number=cfl)
w.integrate(u0, t)
solutions = w.u_grid[:evolve_num + 1, :]
if animation:
return solutions
else:
return solutions[-1]