Dear all, referring to the email below, I removed the phi_nw and phi_old, however, I am not sure where the actual PDE given in the first example at . 58,
d phi/dt = A d^2x∕dx^2 appears in the actual python code. This would be important to change the PDE into other PDEs Where do I define this PDE? Thanks Sergio Manzetti [ http://www.fjordforsk.no/logo_hr2.jpg ] [ http://www.fjordforsk.no/ | Fjordforsk AS ] [ http://www.fjordforsk.no/ | ] Midtun 6894 Vangsnes Norge Org.nr. 911 659 654 Tlf: +47 57695621 [ http://www.oekolab.com/ | Økolab ] | [ http://www.nanofact.no/ | Nanofactory ] | [ http://www.aq-lab.no/ | AQ-Lab ] | [ http://www.phap.no/ | FAP ] From: "sergio manzetti" <sergio.manze...@fjordforsk.no> To: "fipy" <fipy@nist.gov> Sent: Thursday, May 18, 2017 1:36:57 PM Subject: Problems running a simple PDE Hello, following the manual, at the first example with the 1D diffusion, I have tried to make the python script for this (python2.7) and I get a missing name, which is not defined in the example at all. This is the name "cell", which appears on p 58 in the manual. Please see this code which describes this example: Thanks! #Python script for solving a Partial Differential Equation in a diffusion case from fipy import * nx = 50 dx = 1 mesh = Grid1D(nx=nx, dx=dx) phi = CellVariable(name="Solution variable", mesh=mesh, value=0.) #We'll use the coefficient set to D=1 D=1 # We give then 2000 time-steps for the computation, which is defined by 90 percent of the maximum stable timestep, which is given timeStepDuration = 0.9 * dx**2 / (2 * D) steps = 2000 #Then we define the boundary conditions valueLeft = 1 valueRight = 0 #The boundary conditions are represented as faces around the exterior of the mesh, so we define the constraint by the given values on the left and right side of the boundary using the phi.constrain() command phi.constrain(valueLeft, mesh.facesRight) phi.constrain(valueRight, mesh.facesLeft) # We can also omit giving boundary conditions, then the default bc is equivalent to a zero gradient. #At this stage we define the partial differential equation as a numerical problem to be solved for step in range(steps): for j in range(cells): phi_new[j] = phi_old[j] \ + (D * dt / dx**2) * (phi_old[j+1] - 2 * phi_old[j] + phi_old[j-1]) time += dt #and additional code for the boundary conditions eqX = TransientTerm() == ExplicitDiffusionTerm(coeff=D) #We then want to view the results of the calculation and use the command Viewer() for this phiAnalytical = CellVariable(name="analytical value", mesh=mesh) if __name__ == '__main__': viewer = Viewer(vars=(phi, phiAnalytical), datamin=0., datamax=1.) viewer.plot() #If we have a semi-infinite domain, then the solution for this PDE is phi=1-erf(x/2(Dt)^(0.5)). This requires to import SciPy library, so we import that. x = mesh.cellCenters[0] t = timeStepDuration * steps try: from scipy.special import erf phiAnalytical.setValue(1-erf(x / (2 * numerix.sqrt(D * t)))) except ImportError: print ("The Scipy Library is not avaliable to test the solution to the given trasient diffusion equation") # The equation is then solved by repeatedly looping for step in range(steps): eqX.solve(var=phi, dt=timeStepDuration) if __name__ == '__main__': viewer.plot() print (phi.allclose(phiAnalytical, atol = 7e-4)) 1 if __name__ == '__main__': raw_input("Explicit transient diffusion. Press <return> to proceed...")
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