5.4.1. Relaxation of a perturbation

As a first problem class, let us calculate the relaxation of a thin film with a modulation:

class LubricationProblem(Problem):
     def define_problem(self):
             self.add_mesh(LineMesh(N=100)) # simple line mesh
             eqs=LubricationEquations() # equations
             eqs+=TextFileOutput() # output
             eqs+=InitialCondition(h=0.05*(1+0.25*cos(2*pi*var("coordinate_x"))))  # small height with a modulation
             self.add_equations(eqs@"domain") # adding the equation


if __name__=="__main__":
     with LubricationProblem() as problem:
             problem.run(50,outstep=True,startstep=0.25)

The result is depicted in Fig. 5.10.

Relaxation of a perturbed surface $h$ in the lubrication limit

Fig. 5.10 Relaxation of a perturbed surface \(h\) in the lubrication limit.