def grid_reynolds_number(self, u, rho, mu=1, function_space=None):
r''' Compute the grid Reynolds number given by
.. math:: \frac{\rho\|\mathbf{u}\|_2\Delta x}{\mu}
where :math:`\rho` is the density, :math:`\mathbf{u}` is the velocity field,
:math:`\Delta x` is the element size, and :math:`\mu` is the (isotropic) viscosity.
:param ufl.Function u: The velocity field.
:param rho: The density, which can be a constant value or a ufl.Function.
:param ufl.FunctionSpace function_space: The function space in which the grid Reynolds number should be computed.
:param mu: The (isotropic) viscosity. By default, this is set to 1.0.
:returns: A UFL Function representing the grid Reynolds number field.
:rtype: ufl.Function
'''
if(function_space is None):
function_space = FunctionSpace(self.mesh, "CG", 1)
test = TestFunction(function_space)
trial = TrialFunction(function_space)
solution = Function(function_space)
h = CellSize(self.mesh)
magnitude = fields_calculations.magnitude_vector(u, function_space)
a = inner(test, trial)*dx
L = (test*(rho*magnitude*h)/mu)*dx
solve(a == L, solution, bcs=[])
return solution
def grid_reynolds_number(self, u, rho, mu=1, function_space=None):
r''' Compute the grid Reynolds number given by
.. math:: \frac{\rho\|\mathbf{u}\|_2\Delta x}{\mu}
where :math:`\rho` is the density, :math:`\mathbf{u}` is the velocity field,
:math:`\Delta x` is the element size, and :math:`\mu` is the (isotropic) viscosity.
:param ufl.Function u: The velocity field.
:param rho: The density, which can be a constant value or a ufl.Function.
:param ufl.FunctionSpace function_space: The function space in which the grid Reynolds number should be computed.
:param mu: The (isotropic) viscosity. By default, this is set to 1.0.
:returns: A UFL Function representing the grid Reynolds number field.
:rtype: ufl.Function
'''
if (function_space is None):
function_space = FunctionSpace(self.mesh, "CG", 1)
test = TestFunction(function_space)
trial = TrialFunction(function_space)
solution = Function(function_space)
h = CellSize(self.mesh)
magnitude = fields_calculations.magnitude_vector(u, function_space)
a = inner(test, trial) * dx
L = (test * (rho * magnitude * h) / mu) * dx
solve(a == L, solution, bcs=[])
return solution
def courant_number(self, u, dt, function_space=None):
r''' Compute the Courant number given by
.. math:: \frac{\|\mathbf{u}\|_2\Delta t}{\Delta x}
where :math:`\mathbf{u}` is the velocity field, :math:`\Delta t` is the time-step, and :math:`\Delta x` is the element size.
:param ufl.Function u: The velocity field.
:param dt: The time-step size.
:param ufl.FunctionSpace function_space: The function space in which the grid Reynolds number should be computed.
:returns: A UFL Function representing the Courant number field.
:rtype: ufl.Function
'''
if(function_space is None):
function_space = FunctionSpace(self.mesh, "CG", 1)
test = TestFunction(function_space)
trial = TrialFunction(function_space)
solution = Function(function_space)
h = CellSize(self.mesh)
magnitude = fields_calculations.magnitude_vector(u, function_space)
a = inner(test, trial)*dx
L = (test*(magnitude*dt)/h)*dx
solve(a == L, solution, bcs=[])
return solution
def courant_number(self, u, dt, function_space=None):
r''' Compute the Courant number given by
.. math:: \frac{\|\mathbf{u}\|_2\Delta t}{\Delta x}
where :math:`\mathbf{u}` is the velocity field, :math:`\Delta t` is the time-step, and :math:`\Delta x` is the element size.
:param ufl.Function u: The velocity field.
:param dt: The time-step size.
:param ufl.FunctionSpace function_space: The function space in which the grid Reynolds number should be computed.
:returns: A UFL Function representing the Courant number field.
:rtype: ufl.Function
'''
if (function_space is None):
function_space = FunctionSpace(self.mesh, "CG", 1)
test = TestFunction(function_space)
trial = TrialFunction(function_space)
solution = Function(function_space)
h = CellSize(self.mesh)
magnitude = fields_calculations.magnitude_vector(u, function_space)
a = inner(test, trial) * dx
L = (test * (magnitude * dt) / h) * dx
solve(a == L, solution, bcs=[])
return solution
