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