def error(config, eta0, k):
state = Function(config.function_space)
state.interpolate(
SinusoidalInitialCondition(config, eta0, k, config.params["depth"]))
u_exact = "eta0*sqrt(g/depth) * cos(k*x[0]-sqrt(g*depth)*k*t)"
du_exact = "(- eta0*sqrt(g/depth) * sin(k*x[0]-sqrt(g*depth)*k*t) * k)"
eta_exact = "eta0*cos(k*x[0]-sqrt(g*depth)*k*t)"
# The source term
source = Expression((u_exact + " * " + du_exact,
"0.0"), \
eta0=eta0, g=config.params["g"], \
depth=config.params["depth"], t=config.params["current_time"], k=k)
adj_reset()
shallow_water_model.sw_solve(config,
state,
annotate=False,
u_source=source)
analytic_sol = Expression((u_exact, \
"0", \
eta_exact), \
eta0=eta0, g=config.params["g"], \
depth=config.params["depth"], t=config.params["current_time"], k=k)
exactstate = Function(config.function_space)
exactstate.interpolate(analytic_sol)
e = state - exactstate
return sqrt(assemble(dot(e, e) * dx))
def error(config, eta0, k):
state = Function(config.function_space)
state.interpolate(
SinusoidalInitialCondition(config, eta0, k, config.params["depth"]))
u_exact = "eta0*sqrt(g/depth) * cos(k*x[0]-sqrt(g*depth)*k*t)" # The analytical veclocity of the shallow water equations has been multiplied by depth to account for the change of variable (\tilde u = depth u) in this code.
ddu_exact = "(diffusion_coef * eta0*sqrt(g/depth) * cos(k*x[0]-sqrt(g*depth)*k*t) * k*k)"
eta_exact = "eta0*cos(k*x[0]-sqrt(g*depth)*k*t)"
# The source term
source = Expression((ddu_exact,
"0.0"), \
eta0 = eta0, g = config.params["g"], \
depth = config.params["depth"], t = config.params["current_time"], \
k = k, diffusion_coef = config.params["diffusion_coef"])
adj_reset()
shallow_water_model.sw_solve(config,
state,
annotate=False,
u_source=source)
analytic_sol = Expression((u_exact, \
"0", \
eta_exact), \
eta0=eta0, g=config.params["g"], \
depth=config.params["depth"], t=config.params["current_time"], k=k)
exactstate = Function(config.function_space)
exactstate.interpolate(analytic_sol)
e = state - exactstate
return sqrt(assemble(dot(e, e) * dx))
def error(config, eta0, k):
state = Function(config.function_space)
state.interpolate(SinusoidalInitialCondition(config, eta0, k, config.params["depth"]))
adj_reset()
shallow_water_model.sw_solve(config, state, annotate=False)
analytic_sol = Expression(("eta0*sqrt(g/depth)*cos(k*x[0]-sqrt(g*depth)*k*t)", \
"0", \
"eta0*cos(k*x[0]-sqrt(g*depth)*k*t)"), \
eta0=config.params["eta0"], g=config.params["g"], \
depth=config.params["depth"], t=config.params["current_time"], k=config.params["k"])
exactstate = Function(config.function_space)
exactstate.interpolate(analytic_sol)
e = state - exactstate
return sqrt(assemble(dot(e,e)*dx))