Step function parameters

[Ziyan Zhu]

Hello, 

I am a new user of Dedalus. I am wondering if Dedalus can solve an eigenvalue problem or a boundary value problem with a step function parameter. For example, in the following code, instead of 'problem.substitutions['f'] = "1.0" ', I would like to substitute f with a step function of the form of 

f = 0.5 for f < 0

f = 1 for f > 0. 

Is something like this possible? 

Thanks in advance, 

Zoe 

Ny = 51 # number of points in y direction

Ly = 5*np.pi #  width the domain

kmax = np.pi # horizontal wave number extrema

kx_global = np.linspace(-kmax,kmax,100)

# Create bases and domain

y_basis = de.Chebyshev('y', Ny, interval=(-Ly/2, Ly/2)) 

domain = de.Domain([y_basis], grid_dtype=np.complex128, comm=MPI.COMM_SELF) # build a physical domain 

# EVP -> setting up eigenvalue problem 

problem = de.EVP(domain, variables=['u','v','h'], eigenvalue='omega')

# Dirichlet preconditioning that sparifies Dirchlet boundary (interpolation at the Chebyshev interval endpoints)

# Only necessary for Dirichlet boundary condition 

problem.meta[:]['y']['dirichlet'] = True

problem.parameters['Ly'] = Ly

problem.parameters['kx'] = 1 # why do we take kx = 1 but later change kx? 

problem.parameters['pi'] = np.pi

# Use substitutions for x and t derivatives

problem.substitutions['dx(A)'] = "1j*kx*A"

problem.substitutions['dt(A)'] = "-1j*omega*A"

problem.substitutions['w'] = "dx(u) + dy(v)"

problem.substitutions['f'] = "1.0"

problem.add_equation("dt(u) + dx(h) - f * v = 0")

problem.add_equation("dt(v) + dy(h) + f * u = 0")

problem.add_equation("dt(h) + w = 0")

problem.add_bc("left(v) = 0")

problem.add_bc("right(v) = 0")

[Keaton Burns]

Hi Zoe,

First, you could try creating a field for f, setting it to a parametrically smoothed-out step function like tanh or erf, and passing that field into the problem as an NCC parameter.

You could also try using a compound Chebyshev basis, which is two Chebyshev segments stacked next to each other.  Then you could actually make a discontinuous NCC field for f, and pass that in.

-Keaton

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[Ziyan Zhu]

Many thanks for your prompt help, Keaton! 

Best,

Zoe