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##############################################################################
#
# Copyright (c) 2003-2020 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
# Development from 2019 by School of Earth and Environmental Sciences
#
##############################################################################
from __future__ import print_function, division
__copyright__="""Copyright (c) 2003-2020 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
import esys.escriptcore.escriptcpp as escript
import esys.escriptcore.util as util
import esys.escriptcore.linearPDEs as lpe
import math
import sys
class SubSteppingException(Exception):
"""
Thrown if the L{Mountains} class uses substepping.
"""
pass
class Mountains(object):
"""
The Mountains class is defined by the following equations:
(1) eps*w_i,aa+w_i,33=0 where 0<=eps<<1 and a=1,2 and w_i is the extension of the surface velocity where w_i(x_3=1)=v_i.
(2) Integration of topography PDE using Taylor-Galerkin upwinding to stabilize the advection terms
H^(t+dt)=H^t+dt*w_3+w_hat*dt*[(div(w_hat*H^t)+w_3)+(dt/2)+H^t],
where w_hat=w*[1,1,0], dt<0.5*d/max(w_i), d is a characteristic element size; H(x_3=1)=lambda (?)
"""
def __init__(self,domain,eps=0.01):
"""
Sets up the level set method.
:param domain: the domain where the mountains is used
:param eps: the smoothing parameter for (1)
"""
order=escript.Solution(domain).getApproximationOrder()
if order>1:
reduced = True
if escript.ReducedSolution(domain).getApproximationOrder()>1: raise ValueError("Reduced order needs to be equal to 1.")
else:
reduced = False
if eps<0:
raise ValueError("Smooting parameter eps must be non-negative.")
self.__domain = domain
self.__reduced=reduced
self.__DIM=domain.getDim()
z=domain.getX()[self.__DIM-1]
self.__PDE_W = lpe.LinearPDE(domain)
self.__PDE_W.setSymmetryOn()
A=util.kronecker(domain)*eps*0
A[self.__DIM-1,self.__DIM-1]=(0.3*(util.sup(z)-util.inf(z))/util.log(2.))**2
# A[self.__DIM-1,self.__DIM-1]=(sup(FunctionOnBoundary(self.__domain).getSize())/log(2.))**2
self.__PDE_W.setValue(D=1, A=A, q=util.whereZero(util.sup(z)-z)+util.whereZero(util.inf(z)-z))
self.__PDE_H = lpe.LinearPDE(domain)
self.__PDE_H.setSymmetryOn()
if reduced: self.__PDE_H.setReducedOrderOn()
# A=kronecker(domain)*0
# A[self.__DIM-1,self.__DIM-1]=0.1
self.__PDE_H.setValue(D=1.0, q=util.whereZero(util.inf(z)-z))
# self.__PDE_H.getSolverOptions().setSolverMethod(SolverOptions.LUMPING)
self.setVelocity()
self.setTopography()
def getSolverOptionsForSmooting(self):
"""
returns the solver options for the smoothing/extrapolation
"""
return self.__PDE_W.getSolverOptions()
def getSolverOptionsForUpdate(self):
"""
returns the solver options for the topograthy update
"""
return self.__PDE_H.getSolverOptions()
def getDomain(self):
"""
Returns the domain.
"""
return self.__domain
def setVelocity(self,v=None):
"""
set a new velocity. v is define on the entire domain but only the surface values are used.
:param v: velocity field. If None zero is used.
:type v: vector
"""
self.__dt=None
self.__v=escript.Vector(0.,escript.Solution(self.getDomain()))
if not v is None:
xi=self.getDomain().getX()[self.getDomain().getDim()-1]
v=(xi-util.inf(xi))/(util.sup(xi)-util.inf(xi))*v
for d in range(self.__DIM):
self.__PDE_W.setValue(r=v[d])
self.__v[d]=self.__PDE_W.getSolution()
def getVelocity(self):
"""
returns the smoothed/extrapolated velocity
:rtype: vector `Data`
"""
return self.__v
def setTopography(self,H=None):
"""
set the topography to H where H defines the vertical displacement. H is defined for the entire domain.
:param H: the topography. If None zero is used.
:type H: scalar
"""
if self.__reduced:
fs=escript.ReducedSolution(self.getDomain())
else:
fs=escript.Solution(self.getDomain())
if H is None:
self.__H=escript.Scalar(0.0, fs)
else:
self.__H=util.interpolate(H, fs)
def getTopography(self):
"""
returns the current topography.
:rtype: scalar `Data`
"""
return self.__H
def getSafeTimeStepSize(self):
"""
Returns the time step value.
:rtype: ``float``
"""
if self.__dt is None:
h=self.getDomain().getSize()
self.__dt=0.5*util.inf(h/util.length(util.interpolate(self.getVelocity(),h.getFunctionSpace())))
return self.__dt
def update(self,dt=None, allow_substeps=True):
"""
Sets a new W and updates the H function.
:param dt: time step forward. If None the save time step size is used.
:type dt: positve ``float`` which is less or equal than the safe time step size.
"""
if dt is None:
dt = self.getSafeTimeStepSize()
if dt<=0:
raise ValueError("Time step size must be positive.")
dt_safe=self.getSafeTimeStepSize()
n=max(int(math.ceil(dt/dt_safe)+0.5),1)
if n>1 and not allow_substeps:
raise SubSteppingException("Substepping required.")
dt/=n
H=self.getTopography()
w=self.getVelocity()
w_tilda=1.*w
w_tilda[self.__DIM-1]=0
w_z=w[self.__DIM-1]
V=util.vol(self.__PDE_H.getDomain())
t=0
for i in range(n):
# L=util.integrate(w_z*dt+H)/vol(self.__PDE_H.getDomain())
# self.__PDE_H.setValue(X=(inner(w_tilda,grad(H))*dt/2+H)*w_tilda*dt, Y=w_z*dt+H-L)
# H=self.__PDE_H.getSolution()
L=util.integrate(w_z*dt+H)/V
self.__PDE_H.setValue(X=w_tilda*H*(dt/2), Y=w_z*(dt/2)+H-L)
Hhalf=self.__PDE_H.getSolution()
self.__PDE_H.setValue(X=w_tilda*Hhalf*dt, Y=w_z*dt+H-L)
H=self.__PDE_H.getSolution()
print(("DDD : ava = ",util.integrate(H)))
t+=dt
self.setTopography(H)
return self.getTopography()
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