def _calcGeomCoeff(self, var): self._checkCoeff(var) if self.coeff.shape != () and self.coeff.shape[-1] != len(var.mesh.cellVolumes): return self.coeff[..., numerix.newaxis] * CellVariable(mesh=var.mesh, value=var.mesh.cellVolumes) else: return self.coeff * CellVariable(mesh=var.mesh, value=var.mesh.cellVolumes)
def copy(self): """ Copy the value of the `NoiseVariable` to a static `CellVariable`. """ return CellVariable(mesh=self.mesh, name=self.name + "_old", value=self.value, hasOld=0)
def extendVariable(self, extensionVariable, order=2): if not hasattr(self, 'fineDistanceVariable'): self.fineDistanceVariable = DistanceVariable(mesh=self.mesh.fineMesh) if not hasattr(self, 'fineExtensionVariable'): self.fineExtensionVariable = CellVariable(mesh=self.mesh.fineMesh) self.fineDistanceVariable[:] = self(self.mesh.fineMesh.cellCenters) self.fineExtensionVariable[:] = extensionVariable(self.mesh.fineMesh.cellCenters) self.fineDistanceVariable.extendVariable(self.fineExtensionVariable, order=order) extensionVariable[:] = self.fineExtensionVariable(self.mesh.cellCenters)
def _buildAndAddMatrices(self, var, SparseMatrix, boundaryConditions=(), dt=None, transientGeomCoeff=None, diffusionGeomCoeff=None, buildExplicitIfOther=False): """Build matrices of constituent Terms and collect them Only called at top-level by `_prepareLinearSystem()` """ from fipy.matrices.offsetSparseMatrix import OffsetSparseMatrix SparseMatrix = OffsetSparseMatrix(SparseMatrix=SparseMatrix, numberOfVariables=len(self._vars), numberOfEquations=len( self._uncoupledTerms)) matrix = SparseMatrix(mesh=var.mesh) RHSvectors = [] for equationIndex, uncoupledTerm in enumerate(self._uncoupledTerms): SparseMatrix.equationIndex = equationIndex termRHSvector = 0 termMatrix = SparseMatrix(mesh=var.mesh) for varIndex, tmpVar in enumerate(var.vars): SparseMatrix.varIndex = varIndex tmpVar, tmpMatrix, tmpRHSvector = uncoupledTerm._buildAndAddMatrices( tmpVar, SparseMatrix, boundaryConditions=(), dt=dt, transientGeomCoeff=uncoupledTerm._getTransientGeomCoeff( tmpVar), diffusionGeomCoeff=uncoupledTerm._getDiffusionGeomCoeff( tmpVar), buildExplicitIfOther=buildExplicitIfOther) termMatrix += tmpMatrix termRHSvector += tmpRHSvector uncoupledTerm._buildCache(termMatrix, termRHSvector) RHSvectors += [CellVariable(value=termRHSvector, mesh=var.mesh)] matrix += termMatrix return (var, matrix, _CoupledCellVariable(RHSvectors))
def _buildMatrix(self, var, SparseMatrix, boundaryConditions=(), dt=None, transientGeomCoeff=None, diffusionGeomCoeff=None): vec = self.equation.justResidualVector( var=None, boundaryConditions=boundaryConditions, dt=dt) self.coeff = CellVariable(mesh=var.mesh, value=vec * self.underRelaxation) self.geomCoeff = None self.coeffVectors = None return _ExplicitSourceTerm._buildMatrix( self, var=var, SparseMatrix=SparseMatrix, boundaryConditions=boundaryConditions, dt=dt, transientGeomCoeff=transientGeomCoeff, diffusionGeomCoeff=diffusionGeomCoeff)
#Laplacian=0 nx = 50 dx = 1. from fipy.meshes.grid1D import Grid1D mesh = Grid1D(nx=nx, dx=dx) from fipy.variables.cellVariable import CellVariable phi = CellVariable(name="solution variable", mesh=mesh, value=0) z = CellVariable(name="dummy", mesh=mesh, value=0) valueLeft = 1 valueRight = 0 from fipy.boundaryConditions.fixedValue import FixedValue BCs = (FixedValue(faces=mesh.getFacesRight(), value=valueRight), FixedValue(faces=mesh.getFacesLeft(), value=valueLeft)) from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm eqX = ExplicitDiffusionTerm(coeff=1) from fipy import viewers viewer = viewers.make(vars=(phi), limits={'datamin': 0., 'datamax': 1.}) viewer.plot() eqX.solve(var=phi, boundaryConditions=BCs) viewer.plot()
distanceVariable = DistanceVariable( name='level set variable', mesh=mesh, value=numerix.sqrt((mesh.getCellCenters()[:, 0] - L / 2.)**2 + (mesh.getCellCenters()[:, 1] - L / 2.)**2) - initialRadius, hasOld=1) initialSurfactantValue = 1. surfactantVariable = SurfactantVariable(value=initialSurfactantValue, distanceVar=distanceVariable) velocity = CellVariable( name='velocity', mesh=mesh, value=1., ) advectionEquation = buildHigherOrderAdvectionEquation(advectionCoeff=velocity) surfactantEquation = SurfactantEquation(distanceVar=distanceVariable) if __name__ == '__main__': import fipy.viewers distanceViewer = fipy.viewers.make(vars=distanceVariable, limits={ 'datamin': -initialRadius, 'datamax': initialRadius })
newIntensity = np.zeros(nx * ny * nz) mesh = Grid3D(dx, dy, dz, nx, ny, nz) print(intensity.shape) print("Setting phase...") # flatten 3D array to 1D newIntensity = intensity.flatten() print("newIntensity:") print(newIntensity) # set phase t3 = time.time() phase = CellVariable(mesh, value=0.0) phase.setValue(1 - newIntensity / 255) #Thresholding step. Values less than 255 are assigned 0. #empty space 0-254 -> 1 - 0/255 -> 1 #particles 255 -> 1 - 1 -> 0 #sets empty space phase=0, particles phase=1 print("phase:") print(phase) t4 = time.time() print("Phase Set!") # Set diffusivity. print("Setting D...") t5 = time.time()
and (face.getID() in bigMesh.getExteriorFaces())): return 1 else: return 0 def allOthers(face): if ((leftSide(face) or inMiddle(face) or rightSide(face)) or not (face.getID() in bigMesh.getExteriorFaces())): return 0 else: return 1 var = CellVariable(name="concentration", mesh=bigMesh, value=valueLeft) eqn = TransientTerm() == ExplicitDiffusionTerm() exteriorFaces = bigMesh.getExteriorFaces() xFace = exteriorFaces.getCenters()[..., 0] boundaryConditions = ( FixedValue(exteriorFaces.where(xFace**2 < 0.000000000000001), valueLeft), FixedValue(exteriorFaces.where((xFace - (dx * nx))**2 < 0.000000000000001), (valueLeft + valueRight) * 0.5), FixedValue( exteriorFaces.where((xFace - (2 * dx * nx))**2 < 0.000000000000001), valueRight)) answer = numerix.array([
from fipy.terms.transientTerm import TransientTerm from fipy.terms.implicitSourceTerm import ImplicitSourceTerm from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm params = parameters['case 2'] nx = 50 ny = 50 dx = 1. L = nx * dx mesh = Grid2D(nx=nx, ny=ny, dx=dx, dy=1.) shift = 1. KMVar = CellVariable(mesh=mesh, value=params['KM'] * shift, hasOld=1) KCVar = CellVariable(mesh=mesh, value=params['KC'] * shift, hasOld=1) TMVar = CellVariable(mesh=mesh, value=params['TM'] * shift, hasOld=1) TCVar = CellVariable(mesh=mesh, value=params['TC'] * shift, hasOld=1) P3Var = CellVariable(mesh=mesh, value=params['P3'] * shift, hasOld=1) P2Var = CellVariable(mesh=mesh, value=params['P2'] * shift, hasOld=1) RVar = CellVariable(mesh=mesh, value=params['R'], hasOld=1) PN = P3Var + P2Var KMscCoeff = params['chiK'] * (RVar + 1) * (1 - KCVar - KMVar.getCellVolumeAverage()) KMspCoeff = params['lambdaK'] / (1 + PN / params['kappaK']) KMEq = TransientTerm() - KMscCoeff + ImplicitSourceTerm(KMspCoeff) TMscCoeff = params['chiT'] * (1 - TCVar - TMVar.getCellVolumeAverage())
1 """ __docformat__ = 'restructuredtext' from fipy.meshes.grid1D import Grid1D Lx = 1. nx = 100000 dx = Lx / nx mesh = Grid1D(dx=dx, nx=nx) from fipy.tools import numerix from fipy.variables.cellVariable import CellVariable var = CellVariable(mesh=mesh) from fipy.solvers.linearLUSolver import LinearLUSolver from fipy.boundaryConditions.nthOrderBoundaryCondition import NthOrderBoundaryCondition from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm from fipy.terms.transientTerm import TransientTerm eq = ImplicitDiffusionTerm((1.0, 1.0)) BCs = (NthOrderBoundaryCondition(mesh.getFacesLeft(), 0., 0), NthOrderBoundaryCondition(mesh.getFacesRight(), Lx, 0), NthOrderBoundaryCondition(mesh.getFacesLeft(), 0., 2), NthOrderBoundaryCondition(mesh.getFacesRight(), 0., 2)) solver = LinearLUSolver(iterations=10)
def runLeveler(kLeveler=0.018, bulkLevelerConcentration=0.02, cellSize=0.1e-7, rateConstant=0.00026, initialAcceleratorCoverage=0.0, levelerDiffusionCoefficient=5e-10, numberOfSteps=400, displayRate=10, displayViewers=True): kLevelerConsumption = 0.0005 aspectRatio = 1.5 faradaysConstant = 9.6485e4 gasConstant = 8.314 acceleratorDiffusionCoefficient = 4e-10 siteDensity = 6.35e-6 atomicVolume = 7.1e-6 charge = 2 metalDiffusionCoefficient = 4e-10 temperature = 298. overpotential = -0.25 bulkMetalConcentration = 250. bulkAcceleratorConcentration = 50.0e-3 initialLevelerCoverage = 0. cflNumber = 0.2 numberOfCellsInNarrowBand = 20 cellsBelowTrench = 10 trenchDepth = 0.4e-6 trenchSpacing = 0.6e-6 boundaryLayerDepth = 98.7e-6 i0Suppressor = 0.3 i0Accelerator = 22.5 alphaSuppressor = 0.5 alphaAccelerator = 0.4 alphaAdsorption = 0.62 m = 4 b = 2.65 A = 0.3 Ba = -40 Bb = 60 Vd = 0.098 Bd = 0.0008 etaPrime = faradaysConstant * overpotential / gasConstant / temperature from fipy import TrenchMesh from fipy.tools import numerix mesh = TrenchMesh(cellSize=cellSize, trenchSpacing=trenchSpacing, trenchDepth=trenchDepth, boundaryLayerDepth=boundaryLayerDepth, aspectRatio=aspectRatio, angle=numerix.pi * 4. / 180., bowWidth=0., overBumpRadius=0., overBumpWidth=0.) narrowBandWidth = numberOfCellsInNarrowBand * cellSize from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable distanceVar = DistanceVariable(name='distance variable', mesh=mesh, value=-1, narrowBandWidth=narrowBandWidth) distanceVar.setValue(1, where=mesh.getElectrolyteMask()) distanceVar.calcDistanceFunction(narrowBandWidth=1e10) from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable levelerVar = SurfactantVariable(name="leveler variable", value=initialLevelerCoverage, distanceVar=distanceVar) acceleratorVar = SurfactantVariable(name="accelerator variable", value=initialAcceleratorCoverage, distanceVar=distanceVar) from fipy.variables.cellVariable import CellVariable bulkAcceleratorVar = CellVariable(name='bulk accelerator variable', mesh=mesh, value=bulkAcceleratorConcentration) bulkLevelerVar = CellVariable(name='bulk leveler variable', mesh=mesh, value=bulkLevelerConcentration) metalVar = CellVariable(name='metal variable', mesh=mesh, value=bulkMetalConcentration) def depositionCoeff(alpha, i0): expo = numerix.exp(-alpha * etaPrime) return 2 * i0 * (expo - expo * numerix.exp(etaPrime)) coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor) coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator) exchangeCurrentDensity = acceleratorVar.getInterfaceVar() * ( coeffAccelerator - coeffSuppressor) + coeffSuppressor currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant extensionVelocityVariable = CellVariable(name='extension velocity', mesh=mesh, value=depositionRateVariable) from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \ import AdsorbingSurfactantEquation kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime) kAcceleratorConsumption = Bd + A / (numerix.exp(Ba * (overpotential + Vd)) + numerix.exp(Bb * (overpotential + Vd))) q = m * overpotential + b levelerSurfactantEquation = AdsorbingSurfactantEquation( levelerVar, distanceVar=distanceVar, bulkVar=bulkLevelerVar, rateConstant=kLeveler, consumptionCoeff=kLevelerConsumption * depositionRateVariable) accVar1 = acceleratorVar.getInterfaceVar() accVar2 = (accVar1 > 0) * accVar1 accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1)) acceleratorSurfactantEquation = AdsorbingSurfactantEquation( acceleratorVar, distanceVar=distanceVar, bulkVar=bulkAcceleratorVar, rateConstant=kAccelerator, otherVar=levelerVar, otherBulkVar=bulkLevelerVar, otherRateConstant=kLeveler, consumptionCoeff=accConsumptionCoeff) from fipy.models.levelSet.advection.higherOrderAdvectionEquation \ import buildHigherOrderAdvectionEquation advectionEquation = buildHigherOrderAdvectionEquation( advectionCoeff=extensionVelocityVariable) from fipy.boundaryConditions.fixedValue import FixedValue from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \ import buildMetalIonDiffusionEquation metalEquation = buildMetalIonDiffusionEquation( ionVar=metalVar, distanceVar=distanceVar, depositionRate=depositionRateVariable, diffusionCoeff=metalDiffusionCoefficient, metalIonMolarVolume=atomicVolume) metalEquationBCs = FixedValue(mesh.getTopFaces(), bulkMetalConcentration) from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \ import buildSurfactantBulkDiffusionEquation bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation( bulkVar=bulkAcceleratorVar, distanceVar=distanceVar, surfactantVar=acceleratorVar, otherSurfactantVar=levelerVar, diffusionCoeff=acceleratorDiffusionCoefficient, rateConstant=kAccelerator * siteDensity) bulkAcceleratorEquationBCs = (FixedValue(mesh.getTopFaces(), bulkAcceleratorConcentration), ) bulkLevelerEquation = buildSurfactantBulkDiffusionEquation( bulkVar=bulkLevelerVar, distanceVar=distanceVar, surfactantVar=levelerVar, diffusionCoeff=levelerDiffusionCoefficient, rateConstant=kLeveler * siteDensity) bulkLevelerEquationBCs = (FixedValue(mesh.getTopFaces(), bulkLevelerConcentration), ) eqnTuple = ((advectionEquation, distanceVar, ()), (levelerSurfactantEquation, levelerVar, ()), (acceleratorSurfactantEquation, acceleratorVar, ()), (metalEquation, metalVar, metalEquationBCs), (bulkAcceleratorEquation, bulkAcceleratorVar, bulkAcceleratorEquationBCs), (bulkLevelerEquation, bulkLevelerVar, bulkLevelerEquationBCs)) levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2) totalTime = 0.0 if displayViewers: from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer viewers = (MayaviSurfactantViewer(distanceVar, acceleratorVar.getInterfaceVar(), zoomFactor=1e6, limits={ 'datamax': 0.5, 'datamin': 0.0 }, smooth=1, title='accelerator coverage'), MayaviSurfactantViewer(distanceVar, levelerVar.getInterfaceVar(), zoomFactor=1e6, limits={ 'datamax': 0.5, 'datamin': 0.0 }, smooth=1, title='leveler coverage')) for step in range(numberOfSteps): if displayViewers: if step % displayRate == 0: for viewer in viewers: viewer.plot() if step % levelSetUpdateFrequency == 0: distanceVar.calcDistanceFunction(deleteIslands=True) extensionVelocityVariable.setValue(depositionRateVariable) extOnInt = numerix.where( distanceVar > 0, numerix.where(distanceVar < 2 * cellSize, extensionVelocityVariable, 0), 0) dt = cflNumber * cellSize / numerix.max(extOnInt) id = numerix.max(numerix.nonzero(distanceVar._getInterfaceFlag())) distanceVar.extendVariable(extensionVelocityVariable, deleteIslands=True) extensionVelocityVariable[mesh.getFineMesh().getNumberOfCells():] = 0. for eqn, var, BCs in eqnTuple: var.updateOld() for eqn, var, BCs in eqnTuple: eqn.solve(var, boundaryConditions=BCs, dt=dt) totalTime += dt try: testFile = 'testLeveler.gz' import os import examples.levelSet.electroChem from fipy.tools import dump data = dump.read( os.path.join(examples.levelSet.electroChem.__path__[0], testFile)) N = mesh.getFineMesh().getNumberOfCells() print numerix.allclose(data[:N], levelerVar[:N], rtol=1e-3) except: return 0
#!/usr/bin/env python L = 1.0 N = 40 dL = L / N viscosity = 1. pressureRelaxation = 0.2 velocityRelaxation = 0.5 sweeps=10 from fipy.meshes.grid2D import Grid2D mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) from fipy.variables.cellVariable import CellVariable psi = CellVariable(mesh=mesh, name='stream function') Xhat=(1,0) Yhat=(0,1) u=psi.getGrad().dot(Yhat) v=-psi.getGrad().dot(Xhat) U=psi.getFaceGrad() from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm eq=ImplicitDiffusionTerm(0.00001) \ + u * u.getGrad().dot(Xhat) \ + v * u.getGrad().dot(Yhat) \ - 2 * u.getGrad().dot(Yhat).getGrad().dot(Yhat)
for b in grid.boundaries(): gr = boundGrad2[b.id()] # gr = c.grad(c.center(), pN) ax.arrow(b.center()[0], b.center()[1], gr[0], gr[1], color='green') ax.set_xlim([-0.5, 3.5]) ax.set_ylim([-0.5, 3.1]) # F = grid.grad(pot) # print(F) print("div:", divergence(grid, boundGrad)) sys.path.append('/home/carsten/src/fipy') mesh = Grid2D(nx=3, ny=2) val = np.arange(3 * 2.) var = CellVariable(mesh=mesh, value=val) print(var.faceGrad._calcValueNoInline()) print('-____________') # print(var.faceGrad) print(var.faceGrad.divergence) # print(var.__pos__) # [ 4. 3. 2. -2. -3. -4.] ax, cbar = show(grid, np.array(var)) show(grid, axes=ax) X, Y = mesh.getCellCenters() gr = var.grad.numericValue m = 1 for i in range(len(X)): ax.arrow(X[i], Y[i], gr[0][i], gr[1][i])
def runSimpleTrenchSystem(faradaysConstant=9.6e4, gasConstant=8.314, transferCoefficient=0.5, rateConstant0=1.76, rateConstant3=-245e-6, catalystDiffusion=1e-9, siteDensity=9.8e-6, molarVolume=7.1e-6, charge=2, metalDiffusion=5.6e-10, temperature=298., overpotential=-0.3, metalConcentration=250., catalystConcentration=5e-3, catalystCoverage=0., currentDensity0=0.26, currentDensity1=45., cellSize=0.1e-7, trenchDepth=0.5e-6, aspectRatio=2., trenchSpacing=0.6e-6, boundaryLayerDepth=0.3e-6, numberOfSteps=5, displayViewers=True): cflNumber = 0.2 numberOfCellsInNarrowBand = 10 cellsBelowTrench = 10 yCells = cellsBelowTrench \ + int((trenchDepth + boundaryLayerDepth) / cellSize) xCells = int(trenchSpacing / 2 / cellSize) from fipy.meshes.grid2D import Grid2D mesh = Grid2D(dx=cellSize, dy=cellSize, nx=xCells, ny=yCells) narrowBandWidth = numberOfCellsInNarrowBand * cellSize from fipy.models.levelSet.distanceFunction.distanceVariable import \ DistanceVariable distanceVar = DistanceVariable(name='distance variable', mesh=mesh, value=-1, narrowBandWidth=narrowBandWidth, hasOld=1) bottomHeight = cellsBelowTrench * cellSize trenchHeight = bottomHeight + trenchDepth trenchWidth = trenchDepth / aspectRatio sideWidth = (trenchSpacing - trenchWidth) / 2 x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1] distanceVar.setValue(1, where=(y > trenchHeight) | ((y > bottomHeight) & (x < xCells * cellSize - sideWidth))) distanceVar.calcDistanceFunction(narrowBandWidth=1e10) from fipy.models.levelSet.surfactant.surfactantVariable import \ SurfactantVariable catalystVar = SurfactantVariable(name="catalyst variable", value=catalystCoverage, distanceVar=distanceVar) from fipy.variables.cellVariable import CellVariable bulkCatalystVar = CellVariable(name='bulk catalyst variable', mesh=mesh, value=catalystConcentration) metalVar = CellVariable(name='metal variable', mesh=mesh, value=metalConcentration) expoConstant = -transferCoefficient * faradaysConstant \ / (gasConstant * temperature) tmp = currentDensity1 * catalystVar.getInterfaceVar() exchangeCurrentDensity = currentDensity0 + tmp import fipy.tools.numerix as numerix expo = numerix.exp(expoConstant * overpotential) currentDensity = expo * exchangeCurrentDensity * metalVar \ / metalConcentration depositionRateVariable = currentDensity * molarVolume \ / (charge * faradaysConstant) extensionVelocityVariable = CellVariable(name='extension velocity', mesh=mesh, value=depositionRateVariable) from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \ import AdsorbingSurfactantEquation surfactantEquation = AdsorbingSurfactantEquation( surfactantVar=catalystVar, distanceVar=distanceVar, bulkVar=bulkCatalystVar, rateConstant=rateConstant0 + rateConstant3 * overpotential**3) from fipy.models.levelSet.advection.higherOrderAdvectionEquation \ import buildHigherOrderAdvectionEquation advectionEquation = buildHigherOrderAdvectionEquation( advectionCoeff=extensionVelocityVariable) from fipy.boundaryConditions.fixedValue import FixedValue from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \ import buildMetalIonDiffusionEquation metalEquation = buildMetalIonDiffusionEquation( ionVar=metalVar, distanceVar=distanceVar, depositionRate=depositionRateVariable, diffusionCoeff=metalDiffusion, metalIonMolarVolume=molarVolume, ) metalEquationBCs = FixedValue(mesh.getFacesTop(), metalConcentration) from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \ import buildSurfactantBulkDiffusionEquation bulkCatalystEquation = buildSurfactantBulkDiffusionEquation( bulkVar=bulkCatalystVar, distanceVar=distanceVar, surfactantVar=catalystVar, diffusionCoeff=catalystDiffusion, rateConstant=rateConstant0 * siteDensity) catalystBCs = FixedValue(mesh.getFacesTop(), catalystConcentration) if displayViewers: try: from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer viewers = (MayaviSurfactantViewer(distanceVar, catalystVar.getInterfaceVar(), zoomFactor=1e6, limits={ 'datamax': 0.5, 'datamin': 0.0 }, smooth=1, title='catalyst coverage'), ) except: from fipy.viewers import make viewers = (make(distanceVar, limits={ 'datamin': -1e-9, 'datamax': 1e-9 }), make(catalystVar.getInterfaceVar())) else: viewers = () levelSetUpdateFrequency = int(0.8 * narrowBandWidth \ / (cellSize * cflNumber * 2)) for step in range(numberOfSteps): if step % 5 == 0: for viewer in viewers: viewer.plot() if step % levelSetUpdateFrequency == 0: distanceVar.calcDistanceFunction() extensionVelocityVariable.setValue(depositionRateVariable()) distanceVar.updateOld() catalystVar.updateOld() metalVar.updateOld() bulkCatalystVar.updateOld() distanceVar.extendVariable(extensionVelocityVariable) dt = cflNumber * cellSize / numerix.max(extensionVelocityVariable) advectionEquation.solve(distanceVar, dt=dt) surfactantEquation.solve(catalystVar, dt=dt) metalEquation.solve(metalVar, dt=dt, boundaryConditions=metalEquationBCs) bulkCatalystEquation.solve(bulkCatalystVar, dt=dt, boundaryConditions=catalystBCs) try: import os import examples.levelSet.electroChem filepath = os.path.join(examples.levelSet.electroChem.__path__[0], 'test.gz') from fipy.tools import dump from fipy.tools import numerix print catalystVar.allclose(numerix.array(dump.read(filepath)), rtol=1e-4) except: return 0
distanceVar.setValue(1, where=(y > trenchHeight) | ((y > bottomHeight) & (x < xCells * cellSize - sideWidth))) distanceVar.calcDistanceFunction(narrowBandWidth=1e10) from fipy.models.levelSet.surfactant.surfactantVariable import \ SurfactantVariable catalystVar = SurfactantVariable(name="catalyst variable", value=catalystCoverage, distanceVar=distanceVar) from fipy.variables.cellVariable import CellVariable bulkCatalystVar = CellVariable(name='bulk catalyst variable', mesh=mesh, value=catalystConcentration) from fipy.variables.cellVariable import CellVariable metalVar = CellVariable(name='metal variable', mesh=mesh, value=bulkMetalConcentration) bench.stop('variables') bench.start() expoConstant = -transferCoefficient * faradaysConstant \ / (gasConstant * temperature) tmp = currentDensity1 \
def _calcValue(self): mesh = self.var.mesh volumes = CellVariable(mesh=mesh, value=mesh.cellVolumes) return (self.var * volumes).sum() / volumes.sum()
bench.stop('mesh') bench.start() timeStepDuration = 5e-5 tau = 3e-4 alpha = 0.015 c = 0.02 N = 4. kappa1 = 0.9 kappa2 = 20. tempDiffusionCoeff = 2.25 theta = 0. from fipy.variables.cellVariable import CellVariable phase = CellVariable(name='phase field', mesh=mesh, hasOld=1) x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1] phase.setValue(1., where=(x - seedCenter[0])**2 + (y - seedCenter[1])**2 < radius**2) temperature = CellVariable(name='temperature', mesh=mesh, value=initialTemperature, hasOld=1) bench.stop('variables') bench.start() from fipy.tools import numerix mVar = phase - 0.5 - kappa1 / numerix.pi * \
dx = 2. dy = 2. L = dx * nx asq = 1.0 epsilon = 1 diffusionCoeff = 1 from fipy.meshes.grid2D import Grid2D mesh = Grid2D(dx, dy, nx, ny) from fipy.variables.cellVariable import CellVariable from fipy.tools.numerix import random var = CellVariable(name="phase field", mesh=mesh, value=random.random(nx * ny)) faceVar = var.getArithmeticFaceValue() doubleWellDerivative = asq * (1 - 6 * faceVar * (1 - faceVar)) from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm from fipy.terms.transientTerm import TransientTerm diffTerm2 = ImplicitDiffusionTerm(coeff=(diffusionCoeff * doubleWellDerivative, )) diffTerm4 = ImplicitDiffusionTerm(coeff=(diffusionCoeff, -epsilon**2)) eqch = TransientTerm() - diffTerm2 - diffTerm4 from fipy.solvers.linearPCGSolver import LinearPCGSolver from fipy.solvers.linearLUSolver import LinearLUSolver ##solver = LinearLUSolver(tolerance = 1e-15,steps = 1000) solver = LinearPCGSolver(tolerance=1e-15, steps=1000)
import sys from fipy.tools import numerix valueLeft = 0. valueRight = 1. import examples.diffusion.steadyState.mesh20x20 import os.path mesh = GmshImporter2D( os.path.join(examples.diffusion.steadyState.mesh20x20.__path__[0], 'modifiedMesh.msh')) ## "%s/%s" % (sys.__dict__['path'][0], "examples/diffusion/steadyState/mesh20x20/modifiedMesh.msh")) var = CellVariable(name="solution variable", mesh=mesh, value=valueLeft) exteriorFaces = mesh.getExteriorFaces() xFace = exteriorFaces.getCenters()[..., 0] boundaryConditions = (FixedValue( exteriorFaces.where(xFace**2 < 0.000000000000001), valueLeft), FixedValue( exteriorFaces.where( (xFace - 20)**2 < 0.000000000000001), valueRight)) if __name__ == '__main__': ImplicitDiffusionTerm().solve(var, boundaryConditions=boundaryConditions) viewer = fipy.viewers.make(vars=var) viewer.plot() varArray = numerix.array(var)
def runGold(faradaysConstant=9.6e4, consumptionRateConstant=2.6e+6, molarVolume=10.21e-6, charge=1.0, metalDiffusion=1.7e-9, metalConcentration=20.0, catalystCoverage=0.15, currentDensity0=3e-2 * 16, currentDensity1=6.5e-1 * 16, cellSize=0.1e-7, trenchDepth=0.2e-6, aspectRatio=1.47, trenchSpacing=0.5e-6, boundaryLayerDepth=90.0e-6, numberOfSteps=10, taperAngle=6.0, displayViewers=True): cflNumber = 0.2 numberOfCellsInNarrowBand = 20 cellsBelowTrench = 10 from fipy.tools import numerix from fipy import TrenchMesh mesh = TrenchMesh(cellSize=cellSize, trenchSpacing=trenchSpacing, trenchDepth=trenchDepth, boundaryLayerDepth=boundaryLayerDepth, aspectRatio=aspectRatio, angle=numerix.pi * taperAngle / 180., bowWidth=0., overBumpRadius=0., overBumpWidth=0.) narrowBandWidth = numberOfCellsInNarrowBand * cellSize from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable distanceVar = DistanceVariable(name='distance variable', mesh=mesh, value=-1, narrowBandWidth=narrowBandWidth) distanceVar.setValue(1, where=mesh.getElectrolyteMask()) distanceVar.calcDistanceFunction(narrowBandWidth=1e10) from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable catalystVar = SurfactantVariable(name="catalyst variable", value=catalystCoverage, distanceVar=distanceVar) from fipy.variables.cellVariable import CellVariable metalVar = CellVariable(name='metal variable', mesh=mesh, value=metalConcentration) exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.getInterfaceVar( ) currentDensity = metalVar / metalConcentration * exchangeCurrentDensity depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant extensionVelocityVariable = CellVariable(name='extension velocity', mesh=mesh, value=depositionRateVariable) from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \ import AdsorbingSurfactantEquation catalystSurfactantEquation = AdsorbingSurfactantEquation( catalystVar, distanceVar=distanceVar, bulkVar=0, rateConstant=0, consumptionCoeff=consumptionRateConstant * extensionVelocityVariable) from fipy.models.levelSet.advection.higherOrderAdvectionEquation \ import buildHigherOrderAdvectionEquation advectionEquation = buildHigherOrderAdvectionEquation( advectionCoeff=extensionVelocityVariable) from fipy.boundaryConditions.fixedValue import FixedValue from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \ import buildMetalIonDiffusionEquation metalEquation = buildMetalIonDiffusionEquation( ionVar=metalVar, distanceVar=distanceVar, depositionRate=depositionRateVariable, diffusionCoeff=metalDiffusion, metalIonMolarVolume=molarVolume) metalEquationBCs = FixedValue(mesh.getTopFaces(), metalConcentration) if displayViewers: try: from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer viewers = (MayaviSurfactantViewer(distanceVar, catalystVar.getInterfaceVar(), zoomFactor=1e6, limits={ 'datamax': 1.0, 'datamin': 0.0 }, smooth=1, title='catalyst coverage'), ) except: class PlotVariable(CellVariable): def __init__(self, var=None, name=''): CellVariable.__init__(self, mesh=mesh.getFineMesh(), name=name) self.var = self._requires(var) def _calcValue(self): return numerix.array( self.var[:self.mesh.getNumberOfCells()]) from fipy.viewers import make viewers = (make(PlotVariable(var=distanceVar), limits={ 'datamax': 1e-9, 'datamin': -1e-9 }), make(PlotVariable(var=catalystVar.getInterfaceVar()))) else: viewers = () levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2) step = 0 while step < numberOfSteps: if step % 10 == 0: for viewer in viewers: viewer.plot() if step % levelSetUpdateFrequency == 0: distanceVar.calcDistanceFunction(deleteIslands=True) extensionVelocityVariable.setValue( numerix.array(depositionRateVariable)) argmax = numerix.argmax(extensionVelocityVariable) dt = cflNumber * cellSize / extensionVelocityVariable[argmax] distanceVar.extendVariable(extensionVelocityVariable, deleteIslands=True) distanceVar.updateOld() catalystVar.updateOld() metalVar.updateOld() advectionEquation.solve(distanceVar, dt=dt) catalystSurfactantEquation.solve(catalystVar, dt=dt) metalEquation.solve(metalVar, boundaryConditions=metalEquationBCs, dt=dt) step += 1 try: from fipy.tools import dump import os import examples.levelSet.electroChem data = dump.read( os.path.join(examples.levelSet.electroChem.__path__[0], 'goldData.gz')) n = mesh.getFineMesh().getNumberOfCells() print numerix.allclose(catalystVar[:n], data[:n], atol=1.0) except: return 0
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm nx = 10 ny = 5 nz = 3 dx = 1. dy = 1. dz = 1. valueBottomTop = 0. valueLeftRight = 1. mesh = Grid3D(dx=dx, dy=dy, dz=dz, nx=nx, ny=ny, nz=nz) var = CellVariable(name="solution variable", mesh=mesh, value=valueBottomTop) boundaryConditions = (FixedValue(mesh.getFacesLeft(), valueLeftRight), FixedValue(mesh.getFacesRight(), valueLeftRight), FixedValue(mesh.getFacesTop(), valueBottomTop), FixedValue(mesh.getFacesBottom(), valueBottomTop)) #do the 2D problem for comparison nx = 10 ny = 5 dx = 1. dy = 1. mesh2 = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
valueLeft = 0. valueRight = 1. meshList = [] RMSNonOrthoList = [] RMSErrorList = [] for i in range(1, 501): meshList = meshList + [ SkewedGrid2D(dx=1.0, dy=1.0, nx=20, ny=20, rand=(0.001 * i)) ] for mesh in meshList: var = CellVariable(name="solution variable", mesh=mesh, value=valueLeft) from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm ImplicitDiffusionTerm().solve( var, boundaryConditions=(FixedValue(mesh.getFacesLeft(), valueLeft), FixedValue(mesh.getFacesRight(), valueRight))) varArray = numerix.array(var) x = mesh.getCellCenters()[:, 0] analyticalArray = valueLeft + (valueRight - valueLeft) * x / 20 errorArray = varArray - analyticalArray nonOrthoArray = mesh._getNonOrthogonality() RMSError = (numerix.add.reduce(errorArray * errorArray) /
## build the mesh from fipy.meshes.grid1D import Grid1D dx = L / (nx - 1.5) mesh = Grid1D(nx=nx, dx=dx) ## build the distance variable value = mesh.getCellCenters()[:, 0] - 1.499 * dx ##distanceVar = DistanceVariable(mesh = mesh, value = dx * (numerix.arange(nx) - 0.999)) distanceVar = DistanceVariable(mesh=mesh, value=value, hasOld=1) ## Build the bulk diffusion equation bulkVar = CellVariable(mesh=mesh, value=cinf) surfactantVar = SurfactantVariable(distanceVar=distanceVar) bulkEqn = buildSurfactantBulkDiffusionEquation(bulkVar, distanceVar=distanceVar, surfactantVar=surfactantVar, diffusionCoeff=diffusion, rateConstant=rateConstant * siteDensity) bcs = (FixedValue(mesh.getFacesRight(), cinf), ) ## Build the surfactant equation surfEqn = AdsorbingSurfactantEquation(surfactantVar=surfactantVar,
valueLeft = 0. valueRight = 0. L = 10. nx = 400 dx = L / nx cfl = 0.01 velocity = 1. timeStepDuration = cfl * dx / abs(velocity) steps = 1000 mesh = Grid1D(dx=dx, nx=nx) startingArray = numerix.zeros(nx, 'd') startingArray[50:90] = 1. var = CellVariable(name="advection variable", mesh=mesh, value=startingArray) boundaryConditions = (FixedValue(mesh.getFacesLeft(), valueLeft), FixedValue(mesh.getFacesRight(), valueRight)) from fipy.terms.transientTerm import TransientTerm from fipy.terms.powerLawConvectionTerm import PowerLawConvectionTerm eq = TransientTerm() - PowerLawConvectionTerm(coeff=(velocity, )) if __name__ == '__main__': viewer = fipy.viewers.make(vars=(var, )) viewer.plot() raw_input("press key to continue") for step in range(steps):
velocity = 1.0 dt = cfl * dx / velocity steps = int(L / 4. / dt / velocity) from fipy.meshes.grid1D import Grid1D mesh = Grid1D(dx=dx, nx=nx) from fipy.meshes.periodicGrid1D import PeriodicGrid1D periodicMesh = PeriodicGrid1D(dx=dx, nx=nx / 2) startingArray = numerix.zeros(nx, 'd') startingArray[2 * nx / 10:3 * nx / 10] = 1. from fipy.variables.cellVariable import CellVariable var1 = CellVariable(name="non-periodic", mesh=mesh, value=startingArray) var2 = CellVariable(name="periodic", mesh=periodicMesh, value=startingArray[:nx / 2]) from fipy.terms.transientTerm import TransientTerm from fipy.terms.vanLeerConvectionTerm import VanLeerConvectionTerm eq1 = TransientTerm() - VanLeerConvectionTerm(coeff=(-velocity, )) eq2 = TransientTerm() - VanLeerConvectionTerm(coeff=(-velocity, )) if __name__ == '__main__': import fipy.viewers viewer1 = fipy.viewers.make(vars=var1) viewer2 = fipy.viewers.make(vars=var2)
def cellCenters(self): from fipy.variables.cellVariable import CellVariable return CellVariable(mesh=self, value=self._scaledCellCenters, rank=1)
#!/usr/bin/env python L = 1.0 N = 10 dL = L / N viscosity = 1. pressureRelaxation = 0.2 velocityRelaxation = 0.5 sweeps = 10 from fipy.meshes.grid2D import Grid2D mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) from fipy.variables.cellVariable import CellVariable u = CellVariable(mesh=mesh, name='X velocity') v = CellVariable(mesh=mesh, name='Y velocity') from fipy.variables.vectorFaceVariable import VectorFaceVariable velocity = VectorFaceVariable(mesh=mesh) Xhat = (1, 0) Yhat = (0, 1) velocity = u.getFaceGrad().dot(Xhat) * Xhat + v.getFaceGrad().dot(Yhat) * Yhat from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm diffTerm = ImplicitDiffusionTerm(coeff=viscosity) from fipy.terms.exponentialConvectionTerm import ExponentialConvectionTerm
temperature = 1. phaseTransientCoeff = 0.1 epsilon = 0.008 s = 0.01 alpha = 0.015 temperature = 1. dx = L / nx from fipy.meshes.grid1D import Grid1D mesh = Grid1D(dx=dx, nx=nx) from fipy.variables.cellVariable import CellVariable phase = CellVariable(name='PhaseField', mesh=mesh, value=1.) from fipy.variables.modularVariable import ModularVariable theta = ModularVariable(name='Theta', mesh=mesh, value=1.) theta.setValue(0., where=mesh.getCellCenters()[..., 0] > L / 2.) from fipy.terms.implicitSourceTerm import ImplicitSourceTerm mPhiVar = phase - 0.5 + temperature * phase * (1 - phase) thetaMag = theta.getOld().getGrad().getMag() implicitSource = mPhiVar * (phase - (mPhiVar < 0)) implicitSource += (2 * s + epsilon**2 * thetaMag) * thetaMag from fipy.terms.transientTerm import TransientTerm from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
nx = 10 ny = 10 nz = 10 dx = 1. dy = 1. dz = 1. valueFront = 0. valueBack = 10. valueSides = 5. mesh = Grid3D(dx=dx, dy=dy, dz=dz, nx=nx, ny=ny, nz=nz) var = CellVariable(name="variable", mesh=mesh, value=valueSides) ##viewer1 = Grid3DPyxViewer(var, zvalue = 1.0) ##viewer3 = Grid3DPyxViewer(var, zvalue = 3.0) ##viewer5 = Grid3DPyxViewer(var, zvalue = 5.0) ##viewer7 = Grid3DPyxViewer(var, zvalue = 7.0) ##viewer9 = Grid3DPyxViewer(var, zvalue = 9.0) ## from fipy import viewers ## viewer = viewers.make(vars = var) ## viewer.plot() from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm ImplicitDiffusionTerm().solve(var,