def __init__(self, pde, mesh, p):
self.space = ScaledMonomialSpace2d(mesh,p)
self.mesh = mesh
self.pde = pde
self.cellbarycenter = mesh.entity_barycenter('cell')
self.p = p
self.cellmeasure = mesh.entity_measure('cell')
def __init__(self):
self.domain = [0, 50, 0, 50]
self.mesh = MeshFactory().regular(self.domain, n=50)
self.timeline = UniformTimeLine(0, 1, 100)
self.space0 = RaviartThomasFiniteElementSpace2d(self.mesh, p=0)
self.space1 = ScaledMonomialSpace2d(self.mesh, p=1) # 线性间断有限元空间
self.vh = self.space0.function() # 速度
self.ph = self.space0.smspace.function() # 压力
self.ch = self.space1.function(dim=3) # 三个组分的摩尔密度
self.options = {
'viscosity': 1.0,
'permeability': 1.0,
'temperature': 397,
'pressure': 50,
'porosity': 0.2,
'injecttion_rate': 0.1,
'compressibility': (0.001, 0.001, 0.001),
'pmv': (1.0, 1.0, 1.0),
'dt': self.timeline.dt
}
c = self.options['viscosity'] / self.options['permeability']
self.A = c * self.space0.mass_matrix()
self.B = self.space0.div_matrix()
phi = self.options['porosity']
self.M = phi / dt * self.space0.smspace.mass_matrix() #
self.MC = self.space1.cell_mass_matrix() / dt
def __init__(self,
vdata,
cdata,
mesh,
timeline,
p=0,
options={'rdir': '/home/why/result'}):
self.options = options
self.vdata = vdata
self.cdata = cdata
self.mesh = mesh
self.timeline = timeline
self.uspace = RaviartThomasFiniteElementSpace2d(mesh, p=p)
self.cspace = ScaledMonomialSpace2d(mesh, p=p + 1)
self.uh = self.uspace.function() # 速度场自由度数组
self.ph = self.uspace.smspace.function() # 压力场自由度数组
self.ch = self.cspace.function() # 浓度场自由度数组
# 初始浓度场设为 1
ldof = self.cspace.number_of_local_dofs()
self.ch[0::ldof] = 1.0
self.M = self.cspace.cell_mass_matrix()
self.H = inv(self.M)
self.set_init_velocity_field() # 计算初始的速度场和压力场
# vtk 文件输出
node, cell, cellType, NC = self.mesh.to_vtk()
self.points = vtk.vtkPoints()
self.points.SetData(vnp.numpy_to_vtk(node))
self.cells = vtk.vtkCellArray()
self.cells.SetCells(NC, vnp.numpy_to_vtkIdTypeArray(cell))
self.cellType = cellType
def stokes_equation_test(self, p=2, maxit=4):
from scipy.sparse import bmat
from fealpy.pde.Stokes_Model_2d import CosSinData
from fealpy.mesh.simple_mesh_generator import triangle
h = 0.4
pde = CosSinData()
error = np.zeros((maxit, ), dtype=np.float)
for i in range(maxit):
mesh = pde.init_mesh(n=i + 2, meshtype='poly')
if 0:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
plt.show()
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
pspace = ScaledMonomialSpace2d(mesh, p - 1)
isBdDof = uspace.boundary_dof()
udof = uspace.number_of_global_dofs()
pdof = pspace.number_of_global_dofs()
uh = uspace.function()
ph = pspace.function()
uspace.set_dirichlet_bc(uh, pde.dirichlet)
A = uspace.matrix_A()
P = uspace.matrix_P()
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T], [P, None]], format='csr')
FF = np.block([F, np.zeros(pdof, dtype=uspace.ftype)])
x = np.block([uh.T.flat, ph])
isBdDof = np.block(
[isBdDof, isBdDof,
np.zeros(pdof, dtype=np.bool)])
gdof = 2 * udof + pdof
FF -= AA @ x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
AA = T @ AA @ T + Tbd
FF[isBdDof] = x[isBdDof]
x[:] = spsolve(AA, FF)
uh[:, 0] = x[:udof]
uh[:, 1] = x[udof:2 * udof]
ph[:] = x[2 * udof:]
up = uspace.project_to_smspace(uh)
integralalg = uspace.integralalg
error[i] = integralalg.L2_error(pde.velocity, up)
h /= 2
print(error)
print(error[0:-1] / error[1:])
def one_cell_test_0(self, p=2):
from fealpy.pde.stokes_model_2d import StokesModelData_7
pde = StokesModelData_7()
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)], dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
uspace = DivFreeNonConformingVirtualElementSpace2d(mesh, p)
pspace = ScaledMonomialSpace2d(mesh, p - 1)
ldof = pspace.number_of_local_dofs()
isBdDof = uspace.boundary_dof()
udof = uspace.number_of_global_dofs()
pdof = pspace.number_of_global_dofs()
uh = uspace.function()
ph = pspace.function()
uspace.set_dirichlet_bc(uh, pde.dirichlet)
A = uspace.matrix_A()
P = uspace.matrix_P()
C = uspace.CM[:, 0, :ldof].reshape(-1)
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T, None], [P, None, C[:, None]], [None, C, None]],
format='csr')
FF = np.block([F, np.zeros(pdof + 1, dtype=uspace.ftype)])
x = np.block([uh, ph, np.zeros((1, ), dtype=uspace.ftype)])
isBdDof = np.r_['0', isBdDof, np.zeros(pdof + 1, dtype=np.bool)]
gdof = udof + pdof + 1
FF -= AA @ x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
AA = T @ AA @ T + Tbd
FF[isBdDof] = x[isBdDof]
x[:] = spsolve(AA, FF)
uh[:] = x[:udof]
ph[:] = x[udof:-1]
print('ph:', ph)
print('uh:', uh)
up = uspace.project_to_smspace(uh)
print('up:', up)
integralalg = uspace.integralalg
error = integralalg.L2_error(pde.velocity, up)
print(error)
uv = uspace.project(pde.velocity)
print('uproject:', uv)
up = uspace.project_to_smspace(uv)
print('up', up)
error = integralalg.L2_error(pde.velocity, up)
print(error)
def index2_test(self, p=2):
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
space = ScaledMonomialSpace2d(mesh, 3)
idx = space.index2(p=p)
print("p=", p, "\n", idx)
def edge_mass_matrix_test(self, p=2):
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
space = ScaledMonomialSpace2d(mesh, 3)
print("new: p=", p, "\n", space.edge_mass_matrix(p=p))
print("old: p=", p, "\n", space.edge_mass_matrix_1(p=p))
def __init__(self, model):
self.model = model
self.mesh = model.space_mesh()
self.timeline = model.time_mesh(n=3650)
self.uspace = RaviartThomasFiniteElementSpace2d(self.mesh, p=0)
self.cspace = ScaledMonomialSpace2d(self.mesh, p=1) # 线性间断有限元空间
self.uh = self.uspace.function() # 速度
self.ph = model.init_pressure(self.uspace.smspace) # 初始压力
# 三个组分的摩尔密度, 三个组分一起计算
self.ch = model.init_molar_density(self.cspace)
# TODO：初始化三种物质的浓度
# 1 muPa*s = 1e-11 bar*s = 1e-11*24*3600 bar*d = 8.64e-07 bar*d
# 1 md = 9.869 233e-16 m^2
self.options = {
'viscosity':
1.0, # 粘性系数 1 muPa*s = 1e-6 Pa*s, 1 cP = 10^{−3} Pa⋅s = 1 mPa⋅s
'permeability': 1.0, # 1 md 渗透率, 1 md = 9.869233e-16 m^2
'temperature': 397, # 初始温度 K
'pressure': 50, # bar 初始压力
'porosity': 0.2, # 孔隙度
'injecttion_rate': 0.1, # 注入速率
'compressibility': 0.001, #压缩率
'pmv': (1.0, 1.0, 1.0), # 偏摩尔体积
'rdir': '/home/why/result/test/',
'step': 1
}
self.CM = self.cspace.cell_mass_matrix()
self.H = inv(self.CM)
c = 8.64 / 9.869233 * 1e+9
self.M = c * self.uspace.mass_matrix()
self.B = -self.uspace.div_matrix()
dt = self.timeline.dt
c = self.options['porosity'] * self.options['compressibility'] / dt
self.D = c * self.uspace.smspace.mass_matrix()
# 压力边界条件
self.F0 = -self.uspace.set_neumann_bc(model.pressure_bc,
threshold=model.is_pressure_bc)
# vtk 文件输出
node, cell, cellType, NC = self.mesh.to_vtk()
self.points = vtk.vtkPoints()
self.points.SetData(vnp.numpy_to_vtk(node))
self.cells = vtk.vtkCellArray()
self.cells.SetCells(NC, vnp.numpy_to_vtkIdTypeArray(cell))
self.cellType = cellType
def project_test(self, p=2, m=0):
if m == 0:
node = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
elif m == 1:
pde = CosCosData()
qtree = pde.init_mesh(n=4, meshtype='quadtree')
mesh = qtree.to_polygonmesh()
points = np.array([[(0.5, 0.5), (0.6, 0.6)]], dtype=np.float)
space = ScaledMonomialSpace2d(mesh, p)
gphi = space.grad_basis(points)
print(gphi)
errorMatrix = np.zeros((3, maxit), dtype=np.float)
dof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
#mesh = pde.init_mesh(n=i+2, meshtype='poly')
mesh = pde.init_mesh(n=i + 2, meshtype='quad')
mesh = PolygonMesh.from_mesh(mesh)
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
idof = (p - 2) * (p - 1) // 2
dof[i] = NC
uspace = ReducedDivFreeNonConformingVirtualElementSpace2d(mesh, p, q=6)
pspace = ScaledMonomialSpace2d(mesh, 0)
isBdDof = uspace.boundary_dof()
udof = uspace.number_of_global_dofs()
pdof = pspace.number_of_global_dofs()
uh = uspace.function()
ph = pspace.function()
A = uspace.matrix_A()
P = uspace.matrix_P()
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T], [P, None]], format='csr')
FF = np.block([F, np.zeros(pdof, dtype=uspace.ftype)])
def stokes_equation_test(self, p=2, maxit=4, mtype=1):
from scipy.sparse import bmat
from fealpy.pde.Stokes_Model_2d import CosSinData, PolyY2X2Data
from fealpy.mesh.simple_mesh_generator import triangle
h = 0.4
#pde = CosSinData()
pde = PolyY2X2Data()
error = np.zeros((maxit, ), dtype=np.float)
for i in range(maxit):
if mtype == 0:
node = np.array([(-1, -1), (1, -1), (1, 1), (-1, 1)],
dtype=np.float)
cell = np.array([0, 1, 2, 3], dtype=np.int)
cellLocation = np.array([0, 4], dtype=np.int)
mesh = PolygonMesh(node, cell, cellLocation)
else:
mesh = pde.init_mesh(n=i + 2, meshtype='poly')
NE = mesh.number_of_edges()
NC = mesh.number_of_cells()
idof = (p - 2) * (p - 1) // 2
if True:
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
uspace = ReducedDivFreeNonConformingVirtualElementSpace2d(mesh, p)
pspace = ScaledMonomialSpace2d(mesh, 0)
isBdDof = uspace.boundary_dof()
udof = uspace.number_of_global_dofs()
pdof = pspace.number_of_global_dofs()
uh = uspace.function()
ph = pspace.function()
uspace.set_dirichlet_bc(uh, pde.dirichlet)
A = uspace.matrix_A()
P = uspace.matrix_P()
F = uspace.source_vector(pde.source)
AA = bmat([[A, P.T], [P, None]], format='csr')
FF = np.block([F, np.zeros(pdof, dtype=uspace.ftype)])
x = np.block([uh, ph])
isBdDof = np.block(
[isBdDof, isBdDof,
np.zeros(NC * idof + pdof, dtype=np.bool)])
gdof = udof + pdof
FF -= AA @ x
bdIdx = np.zeros(gdof, dtype=np.int)
bdIdx[isBdDof] = 1
Tbd = spdiags(bdIdx, 0, gdof, gdof)
T = spdiags(1 - bdIdx, 0, gdof, gdof)
AA = T @ AA @ T + Tbd
FF[isBdDof] = x[isBdDof]
x[:] = spsolve(AA, FF)
uh[:] = x[:udof]
ph[:] = x[udof:]
up = uspace.project_to_smspace(uh)
integralalg = uspace.integralalg
error[i] = integralalg.L2_error(pde.velocity, up)
h /= 2
print(error)
print(error[0:-1] / error[1:])
plt.show()
