1D Finite-Volume with adaptive mesh refinement and steady-state solver using Newton and Split-Newton approach

The system is divided into two and for ease of communication, let's refer to first set of variables as "outer" and the second as "inner".

• Holding the outer variables fixed, Newton iteration is performed till convergence using the sub-Jacobian

• One Newton step is performed for the outer variables with inner held fixed (using its sub-Jacobian)

• This process is repeated till convergence criterion is met for the full system (same as in Newton)

Just run

pip install splitfvm

There is an examples folder that contains a test model - Advection-Diffusion

You can define your own equations by simply creating a derived class from Model and adding to the _equations using existing or custom equations!

A basic driver program is as follows

# Define the problem
m = AdvectionDiffusion(c=0.2, nu=0.001)

# Define the domain and variables
# ng stands for ghost cell count
d = Domain.from_size(20, 2, ["u", "v", "w"]) # nx, ng, variables

# Set IC and BC
ics = {"u": "gaussian", "v": "rarefaction"}
bcs = {
    "u": {
        "left": "periodic",
        "right": "periodic"
    },
    "v": {
        "left": {"dirichlet": 3},
        "right": {"dirichlet": 4}
    },
    "w": {
        "left": {"dirichlet": 2},
        "right": "periodic"
    }
}
s = Simulation(d, m, ics, bcs)

# Advance in time or to steady state
s.evolve(dt=0.1)
bounds = [[-1., -2., 0.], [5., 4., 3.]]
iter = s.steady_state(split=True, split_loc=1, bounds=bounds)

# Visualize
draw(d, "label")

Please direct your queries to gpavanb1 for any questions.

Do visit its Finite-Difference cousin

Special thanks to Cantera and WENO-Scalar for serving as an inspiration for code architecture