def setValue(self, value, unit = None, where = None): if where is not None: shape = numerix.getShape(where) if shape != self.shape \ and shape == self._getShapeFromMesh(mesh=self.getMesh()): for dim in self.elementshape: where = numerix.repeat(where[numerix.newaxis, ...], repeats=dim, axis=0) return Variable.setValue(self, value=value, unit=unit, where=where)
def setValue(self, value, unit=None, where=None): if where is not None: shape = numerix.getShape(where) if shape != self.shape \ and shape == self._getShapeFromMesh(mesh=self.mesh): for dim in self.elementshape: where = numerix.repeat(where[numerix.newaxis, ...], repeats=dim, axis=0) return Variable.setValue(self, value=value, unit=unit, where=where)
class AdsorbingSurfactantEquation(): r""" The `AdsorbingSurfactantEquation` object solves the `SurfactantEquation` but with an adsorbing species from some bulk value. The equation that describes the surfactant adsorbing is given by, .. math:: \dot{\theta} = J v \theta + k c (1 - \theta - \theta_{\text{other}}) - \theta c_{\text{other}} k_{\text{other}} - k^- \theta where :math:`\theta`, :math:`J`, :math:`v`, :math:`k`, :math:`c`, :math:`k^-` and :math:`n` represent the surfactant coverage, the curvature, the interface normal velocity, the adsorption rate, the concentration in the bulk at the interface, the consumption rate and an exponent of consumption, respectively. The :math:`\text{other}` subscript refers to another surfactant with greater surface affinity. The terms on the RHS of the above equation represent conservation of surfactant on a non-uniform surface, Langmuir adsorption, removal of surfactant due to adsorption of the other surfactant onto non-vacant sites and consumption of the surfactant respectively. The adsorption term is added to the source by setting :math:` S_c = k c (1 - \theta_{\text{other}})` and :math:`S_p = -k c`. The other terms are added to the source in a similar way. The following is a test case: >>> from fipy.variables.distanceVariable \ ... import DistanceVariable >>> from fipy import SurfactantVariable >>> from fipy.meshes import Grid2D >>> from fipy.tools import numerix >>> from fipy.variables.cellVariable import CellVariable >>> dx = .5 >>> dy = 2.3 >>> dt = 0.25 >>> k = 0.56 >>> initialValue = 0.1 >>> c = 0.2 >>> from fipy.meshes import Grid2D >>> from fipy import serialComm >>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm) >>> distanceVar = DistanceVariable(mesh = mesh, ... value = (-dx*3/2, -dx/2, dx/2, ... 3*dx/2, 5*dx/2), ... hasOld = 1) >>> surfactantVar = SurfactantVariable(value = (0, 0, initialValue, 0 ,0), ... distanceVar = distanceVar) >>> bulkVar = CellVariable(mesh = mesh, value = (c , c, c, c, c)) >>> eqn = AdsorbingSurfactantEquation(surfactantVar = surfactantVar, ... distanceVar = distanceVar, ... bulkVar = bulkVar, ... rateConstant = k) >>> eqn.solve(surfactantVar, dt = dt) >>> answer = (initialValue + dt * k * c) / (1 + dt * k * c) >>> print numerix.allclose(surfactantVar.interfaceVar, ... numerix.array((0, 0, answer, 0, 0))) 1 The following test case is for two surfactant variables. One has more surface affinity than the other. >>> from fipy.variables.distanceVariable \ ... import DistanceVariable >>> from fipy import SurfactantVariable >>> from fipy.meshes import Grid2D >>> dx = 0.5 >>> dy = 2.73 >>> dt = 0.001 >>> k0 = 1. >>> k1 = 10. >>> theta0 = 0. >>> theta1 = 0. >>> c0 = 1. >>> c1 = 1. >>> totalSteps = 10 >>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm) >>> distanceVar = DistanceVariable(mesh = mesh, ... value = dx * (numerix.arange(5) - 1.5), ... hasOld = 1) >>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0), ... distanceVar = distanceVar) >>> var1 = SurfactantVariable(value = (0, 0, theta1, 0 ,0), ... distanceVar = distanceVar) >>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0)) >>> bulkVar1 = CellVariable(mesh = mesh, value = (c1, c1, c1, c1, c1)) >>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0, ... distanceVar = distanceVar, ... bulkVar = bulkVar0, ... rateConstant = k0) >>> eqn1 = AdsorbingSurfactantEquation(surfactantVar = var1, ... distanceVar = distanceVar, ... bulkVar = bulkVar1, ... rateConstant = k1, ... otherVar = var0, ... otherBulkVar = bulkVar0, ... otherRateConstant = k0) >>> for step in range(totalSteps): ... eqn0.solve(var0, dt = dt) ... eqn1.solve(var1, dt = dt) >>> answer0 = 1 - numerix.exp(-k0 * c0 * dt * totalSteps) >>> answer1 = (1 - numerix.exp(-k1 * c1 * dt * totalSteps)) * (1 - answer0) >>> print numerix.allclose(var0.interfaceVar, ... numerix.array((0, 0, answer0, 0, 0)), rtol = 1e-2) 1 >>> print numerix.allclose(var1.interfaceVar, ... numerix.array((0, 0, answer1, 0, 0)), rtol = 1e-2) 1 >>> dt = 0.1 >>> for step in range(10): ... eqn0.solve(var0, dt = dt) ... eqn1.solve(var1, dt = dt) >>> x, y = mesh.cellCenters >>> check = var0.interfaceVar + var1.interfaceVar >>> answer = CellVariable(mesh=mesh, value=check) >>> answer[x==1.25] = 1. >>> print check.allequal(answer) True The following test case is to fix a bug where setting the adsorption coefficient to zero leads to the solver not converging and an eventual failure. >>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0), ... distanceVar = distanceVar) >>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0)) >>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0, ... distanceVar = distanceVar, ... bulkVar = bulkVar0, ... rateConstant = 0) >>> eqn0.solve(var0, dt = dt) >>> eqn0.solve(var0, dt = dt) >>> answer = CellVariable(mesh=mesh, value=var0.interfaceVar) >>> answer[x==1.25] = 0. >>> print var0.interfaceVar.allclose(answer) True The following test case is to fix a bug that allows the accelerator to become negative. >>> nx = 5 >>> ny = 5 >>> dx = 1. >>> dy = 1. >>> mesh = Grid2D(dx=dx, dy=dy, nx = nx, ny = ny, communicator=serialComm) >>> x, y = mesh.cellCenters >>> disVar = DistanceVariable(mesh=mesh, value=1., hasOld=True) >>> disVar[y < dy] = -1 >>> disVar[x < dx] = -1 >>> disVar.calcDistanceFunction() #doctest: +LSM >>> levVar = SurfactantVariable(value = 0.5, distanceVar = disVar) >>> accVar = SurfactantVariable(value = 0.5, distanceVar = disVar) >>> levEq = AdsorbingSurfactantEquation(levVar, ... distanceVar = disVar, ... bulkVar = 0, ... rateConstant = 0) >>> accEq = AdsorbingSurfactantEquation(accVar, ... distanceVar = disVar, ... bulkVar = 0, ... rateConstant = 0, ... otherVar = levVar, ... otherBulkVar = 0, ... otherRateConstant = 0) >>> extVar = CellVariable(mesh = mesh, value = accVar.interfaceVar) >>> from fipy import TransientTerm, AdvectionTerm >>> advEq = TransientTerm() + AdvectionTerm(extVar) >>> dt = 0.1 >>> for i in range(50): ... disVar.calcDistanceFunction() ... extVar.value = (numerix.array(accVar.interfaceVar)) ... disVar.extendVariable(extVar) ... disVar.updateOld() ... advEq.solve(disVar, dt = dt) ... levEq.solve(levVar, dt = dt) ... accEq.solve(accVar, dt = dt) #doctest: +LSM >>> # The following test fails sometimes on linux with scipy solvers >>> # See issue #575. We ignore for now. >>> print (accVar >= -1e-10).all() #doctest: +NOTLINUXSCIPY True """ def __init__(self, surfactantVar=None, distanceVar=None, bulkVar=None, rateConstant=None, otherVar=None, otherBulkVar=None, otherRateConstant=None, consumptionCoeff=None): """ Create a `AdsorbingSurfactantEquation` object. :Parameters: - `surfactantVar`: The `SurfactantVariable` to be solved for. - `distanceVar`: The `DistanceVariable` that marks the interface. - `bulkVar`: The value of the `surfactantVar` in the bulk. - `rateConstant`: The adsorption rate of the `surfactantVar`. - `otherVar`: Another `SurfactantVariable` with more surface affinity. - `otherBulkVar`: The value of the `otherVar` in the bulk. - `otherRateConstant`: The adsorption rate of the `otherVar`. - `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition. """ self.eq = TransientTerm(coeff=1) - ExplicitUpwindConvectionTerm( SurfactantConvectionVariable(distanceVar)) self.dt = Variable(0.) mesh = distanceVar.mesh adsorptionCoeff = self.dt * bulkVar * rateConstant spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes self.eq += ImplicitSourceTerm(spCoeff) - scCoeff if otherVar is not None: otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag otherScCoeff = -otherVar.interfaceVar * scCoeff self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff vars = (surfactantVar, otherVar) else: vars = (surfactantVar, ) total = 0 for var in vars: total += var.interfaceVar maxVar = (total > 1) * distanceVar._cellInterfaceFlag val = distanceVar.cellInterfaceAreas / mesh.cellVolumes for var in vars[1:]: val -= distanceVar._cellInterfaceFlag * var spMaxCoeff = 1e20 * maxVar scMaxCoeff = spMaxCoeff * val * (val > 0) self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40 if consumptionCoeff is not None: self.eq += ImplicitSourceTerm(consumptionCoeff) def solve(self, var, boundaryConditions=(), solver=None, dt=None): """ Builds and solves the `AdsorbingSurfactantEquation`'s linear system once. :Parameters: - `var`: A `SurfactantVariable` to be solved for. Provides the initial condition, the old value and holds the solution on completion. - `solver`: The iterative solver to be used to solve the linear system of equations. - `boundaryConditions`: A tuple of boundaryConditions. - `dt`: The time step size. """ self.dt.setValue(dt) if solver is None: import fipy.solvers.solver if fipy.solvers.solver == 'pyamg': from fipy.solvers.pyAMG.linearGeneralSolver import LinearGeneralSolver solver = LinearGeneralSolver(tolerance=1e-15, iterations=2000) else: from fipy.solvers import LinearPCGSolver solver = LinearPCGSolver() if type(boundaryConditions) not in (type(()), type([])): boundaryConditions = (boundaryConditions, ) var.constrain(0, var.mesh.exteriorFaces) self.eq.solve(var, boundaryConditions=boundaryConditions, solver=solver, dt=1.) def sweep(self, var, solver=None, boundaryConditions=(), dt=None, underRelaxation=None, residualFn=None): r""" Builds and solves the `AdsorbingSurfactantEquation`'s linear system once. This method also recalculates and returns the residual as well as applying under-relaxation. :Parameters: - `var`: The variable to be solved for. Provides the initial condition, the old value and holds the solution on completion. - `solver`: The iterative solver to be used to solve the linear system of equations. - `boundaryConditions`: A tuple of boundaryConditions. - `dt`: The time step size. - `underRelaxation`: Usually a value between `0` and `1` or `None` in the case of no under-relaxation """ self.dt.setValue(dt) if solver is None: from fipy.solvers import DefaultAsymmetricSolver solver = DefaultAsymmetricSolver() if type(boundaryConditions) not in (type(()), type([])): boundaryConditions = (boundaryConditions, ) var.constrain(0, var.mesh.exteriorFaces) return self.eq.sweep(var, solver=solver, boundaryConditions=boundaryConditions, underRelaxation=underRelaxation, residualFn=residualFn, dt=1.)
class AdsorbingSurfactantEquation(): r""" The `AdsorbingSurfactantEquation` object solves the `SurfactantEquation` but with an adsorbing species from some bulk value. The equation that describes the surfactant adsorbing is given by, .. math:: \dot{\theta} = J v \theta + k c (1 - \theta - \theta_{\text{other}}) - \theta c_{\text{other}} k_{\text{other}} - k^- \theta where :math:`\theta`, :math:`J`, :math:`v`, :math:`k`, :math:`c`, :math:`k^-` and :math:`n` represent the surfactant coverage, the curvature, the interface normal velocity, the adsorption rate, the concentration in the bulk at the interface, the consumption rate and an exponent of consumption, respectively. The :math:`\text{other}` subscript refers to another surfactant with greater surface affinity. The terms on the RHS of the above equation represent conservation of surfactant on a non-uniform surface, Langmuir adsorption, removal of surfactant due to adsorption of the other surfactant onto non-vacant sites and consumption of the surfactant respectively. The adsorption term is added to the source by setting :math:` S_c = k c (1 - \theta_{\text{other}})` and :math:`S_p = -k c`. The other terms are added to the source in a similar way. The following is a test case: >>> from fipy.variables.distanceVariable \ ... import DistanceVariable >>> from fipy import SurfactantVariable >>> from fipy.meshes import Grid2D >>> from fipy.tools import numerix >>> from fipy.variables.cellVariable import CellVariable >>> dx = .5 >>> dy = 2.3 >>> dt = 0.25 >>> k = 0.56 >>> initialValue = 0.1 >>> c = 0.2 >>> from fipy.meshes import Grid2D >>> from fipy import serialComm >>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm) >>> distanceVar = DistanceVariable(mesh = mesh, ... value = (-dx*3/2, -dx/2, dx/2, ... 3*dx/2, 5*dx/2), ... hasOld = 1) >>> surfactantVar = SurfactantVariable(value = (0, 0, initialValue, 0 ,0), ... distanceVar = distanceVar) >>> bulkVar = CellVariable(mesh = mesh, value = (c , c, c, c, c)) >>> eqn = AdsorbingSurfactantEquation(surfactantVar = surfactantVar, ... distanceVar = distanceVar, ... bulkVar = bulkVar, ... rateConstant = k) >>> eqn.solve(surfactantVar, dt = dt) >>> answer = (initialValue + dt * k * c) / (1 + dt * k * c) >>> print numerix.allclose(surfactantVar.interfaceVar, ... numerix.array((0, 0, answer, 0, 0))) 1 The following test case is for two surfactant variables. One has more surface affinity than the other. >>> from fipy.variables.distanceVariable \ ... import DistanceVariable >>> from fipy import SurfactantVariable >>> from fipy.meshes import Grid2D >>> dx = 0.5 >>> dy = 2.73 >>> dt = 0.001 >>> k0 = 1. >>> k1 = 10. >>> theta0 = 0. >>> theta1 = 0. >>> c0 = 1. >>> c1 = 1. >>> totalSteps = 10 >>> mesh = Grid2D(dx = dx, dy = dy, nx = 5, ny = 1, communicator=serialComm) >>> distanceVar = DistanceVariable(mesh = mesh, ... value = dx * (numerix.arange(5) - 1.5), ... hasOld = 1) >>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0), ... distanceVar = distanceVar) >>> var1 = SurfactantVariable(value = (0, 0, theta1, 0 ,0), ... distanceVar = distanceVar) >>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0)) >>> bulkVar1 = CellVariable(mesh = mesh, value = (c1, c1, c1, c1, c1)) >>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0, ... distanceVar = distanceVar, ... bulkVar = bulkVar0, ... rateConstant = k0) >>> eqn1 = AdsorbingSurfactantEquation(surfactantVar = var1, ... distanceVar = distanceVar, ... bulkVar = bulkVar1, ... rateConstant = k1, ... otherVar = var0, ... otherBulkVar = bulkVar0, ... otherRateConstant = k0) >>> for step in range(totalSteps): ... eqn0.solve(var0, dt = dt) ... eqn1.solve(var1, dt = dt) >>> answer0 = 1 - numerix.exp(-k0 * c0 * dt * totalSteps) >>> answer1 = (1 - numerix.exp(-k1 * c1 * dt * totalSteps)) * (1 - answer0) >>> print numerix.allclose(var0.interfaceVar, ... numerix.array((0, 0, answer0, 0, 0)), rtol = 1e-2) 1 >>> print numerix.allclose(var1.interfaceVar, ... numerix.array((0, 0, answer1, 0, 0)), rtol = 1e-2) 1 >>> dt = 0.1 >>> for step in range(10): ... eqn0.solve(var0, dt = dt) ... eqn1.solve(var1, dt = dt) >>> x, y = mesh.cellCenters >>> check = var0.interfaceVar + var1.interfaceVar >>> answer = CellVariable(mesh=mesh, value=check) >>> answer[x==1.25] = 1. >>> print check.allequal(answer) True The following test case is to fix a bug where setting the adosrbtion coefficient to zero leads to the solver not converging and an eventual failure. >>> var0 = SurfactantVariable(value = (0, 0, theta0, 0 ,0), ... distanceVar = distanceVar) >>> bulkVar0 = CellVariable(mesh = mesh, value = (c0, c0, c0, c0, c0)) >>> eqn0 = AdsorbingSurfactantEquation(surfactantVar = var0, ... distanceVar = distanceVar, ... bulkVar = bulkVar0, ... rateConstant = 0) >>> eqn0.solve(var0, dt = dt) >>> eqn0.solve(var0, dt = dt) >>> answer = CellVariable(mesh=mesh, value=var0.interfaceVar) >>> answer[x==1.25] = 0. >>> print var0.interfaceVar.allclose(answer) True The following test case is to fix a bug that allows the accelerator to become negative. >>> nx = 5 >>> ny = 5 >>> dx = 1. >>> dy = 1. >>> mesh = Grid2D(dx=dx, dy=dy, nx = nx, ny = ny, communicator=serialComm) >>> x, y = mesh.cellCenters >>> disVar = DistanceVariable(mesh=mesh, value=1., hasOld=True) >>> disVar[y < dy] = -1 >>> disVar[x < dx] = -1 >>> disVar.calcDistanceFunction() #doctest: +LSM >>> levVar = SurfactantVariable(value = 0.5, distanceVar = disVar) >>> accVar = SurfactantVariable(value = 0.5, distanceVar = disVar) >>> levEq = AdsorbingSurfactantEquation(levVar, ... distanceVar = disVar, ... bulkVar = 0, ... rateConstant = 0) >>> accEq = AdsorbingSurfactantEquation(accVar, ... distanceVar = disVar, ... bulkVar = 0, ... rateConstant = 0, ... otherVar = levVar, ... otherBulkVar = 0, ... otherRateConstant = 0) >>> extVar = CellVariable(mesh = mesh, value = accVar.interfaceVar) >>> from fipy import TransientTerm, AdvectionTerm >>> advEq = TransientTerm() + AdvectionTerm(extVar) >>> dt = 0.1 >>> for i in range(50): ... disVar.calcDistanceFunction() ... extVar.value = (numerix.array(accVar.interfaceVar)) ... disVar.extendVariable(extVar) ... disVar.updateOld() ... advEq.solve(disVar, dt = dt) ... levEq.solve(levVar, dt = dt) ... accEq.solve(accVar, dt = dt) #doctest: +LSM >>> print (accVar >= -1e-10).all() True """ def __init__(self, surfactantVar = None, distanceVar = None, bulkVar = None, rateConstant = None, otherVar = None, otherBulkVar = None, otherRateConstant = None, consumptionCoeff = None): """ Create a `AdsorbingSurfactantEquation` object. :Parameters: - `surfactantVar`: The `SurfactantVariable` to be solved for. - `distanceVar`: The `DistanceVariable` that marks the interface. - `bulkVar`: The value of the `surfactantVar` in the bulk. - `rateConstant`: The adsorption rate of the `surfactantVar`. - `otherVar`: Another `SurfactantVariable` with more surface affinity. - `otherBulkVar`: The value of the `otherVar` in the bulk. - `otherRateConstant`: The adsorption rate of the `otherVar`. - `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition. """ self.eq = TransientTerm(coeff = 1) - ExplicitUpwindConvectionTerm(SurfactantConvectionVariable(distanceVar)) self.dt = Variable(0.) mesh = distanceVar.mesh adsorptionCoeff = self.dt * bulkVar * rateConstant spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes self.eq += ImplicitSourceTerm(spCoeff) - scCoeff if otherVar is not None: otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag otherScCoeff = -otherVar.interfaceVar * scCoeff self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff vars = (surfactantVar, otherVar) else: vars = (surfactantVar,) total = 0 for var in vars: total += var.interfaceVar maxVar = (total > 1) * distanceVar._cellInterfaceFlag val = distanceVar.cellInterfaceAreas / mesh.cellVolumes for var in vars[1:]: val -= distanceVar._cellInterfaceFlag * var spMaxCoeff = 1e20 * maxVar scMaxCoeff = spMaxCoeff * val * (val > 0) self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40 if consumptionCoeff is not None: self.eq += ImplicitSourceTerm(consumptionCoeff) def solve(self, var, boundaryConditions=(), solver=None, dt=None): """ Builds and solves the `AdsorbingSurfactantEquation`'s linear system once. :Parameters: - `var`: A `SurfactantVariable` to be solved for. Provides the initial condition, the old value and holds the solution on completion. - `solver`: The iterative solver to be used to solve the linear system of equations. - `boundaryConditions`: A tuple of boundaryConditions. - `dt`: The time step size. """ self.dt.setValue(dt) if solver is None: import fipy.solvers.solver if fipy.solvers.solver == 'pyamg': from fipy.solvers.pyAMG.linearGeneralSolver import LinearGeneralSolver solver = LinearGeneralSolver(tolerance=1e-15, iterations=2000) else: from fipy.solvers import LinearPCGSolver solver = LinearPCGSolver() if type(boundaryConditions) not in (type(()), type([])): boundaryConditions = (boundaryConditions,) var.constrain(0, var.mesh.exteriorFaces) self.eq.solve(var, boundaryConditions=boundaryConditions, solver = solver, dt=1.) def sweep(self, var, solver=None, boundaryConditions=(), dt=None, underRelaxation=None, residualFn=None): r""" Builds and solves the `AdsorbingSurfactantEquation`'s linear system once. This method also recalculates and returns the residual as well as applying under-relaxation. :Parameters: - `var`: The variable to be solved for. Provides the initial condition, the old value and holds the solution on completion. - `solver`: The iterative solver to be used to solve the linear system of equations. - `boundaryConditions`: A tuple of boundaryConditions. - `dt`: The time step size. - `underRelaxation`: Usually a value between `0` and `1` or `None` in the case of no under-relaxation """ self.dt.setValue(dt) if solver is None: from fipy.solvers import DefaultAsymmetricSolver solver = DefaultAsymmetricSolver() if type(boundaryConditions) not in (type(()), type([])): boundaryConditions = (boundaryConditions,) var.constrain(0, var.mesh.exteriorFaces) return self.eq.sweep(var, solver=solver, boundaryConditions=boundaryConditions, underRelaxation=underRelaxation, residualFn=residualFn, dt=1.)