pymor.analyticalproblems.burgers

Module Contents

pymor.analyticalproblems.burgers.burgers_problem(v=1.0, circle=True, initial_data_type='sin', parameter_range=(1.0, 2.0))

One-dimensional Burgers-type problem.

The problem is to solve

∂_t u(x, t, μ)  +  ∂_x (v * u(x, t, μ)^μ) = 0
                               u(x, 0, μ) = u_0(x)

for u with t in [0, 0.3] and x in [0, 2].

Parameters:

• v – The velocity v.

• circle – If True, impose periodic boundary conditions. Otherwise Dirichlet left, outflow right.

• initial_data_type – Type of initial data ('sin' or 'bump').

• parameter_range – The interval in which μ is allowed to vary.

pymor.analyticalproblems.burgers.burgers_problem_2d(vx=1.0, vy=1.0, torus=True, initial_data_type='sin', parameter_range=(1.0, 2.0))

Two-dimensional Burgers-type problem.

The problem is to solve

∂_t u(x, t, μ)  +  ∇ ⋅ (v * u(x, t, μ)^μ) = 0
                               u(x, 0, μ) = u_0(x)

for u with t in [0, 0.3], x in [0, 2] x [0, 1].

Parameters:

• vx – The x component of the velocity vector v.

• vy – The y component of the velocity vector v.

• torus – If True, impose periodic boundary conditions. Otherwise, Dirichlet left and bottom, outflow top and right.

• initial_data_type – Type of initial data ('sin' or 'bump').

• parameter_range – The interval in which μ is allowed to vary.