1-dimensional acoustics

One-dimensional acoustics

Solve the (linear) acoustics equations:

\[\begin{split}p_t + K u_x & = 0 \\ u_t + p_x / \rho & = 0.\end{split}\]

Here p is the pressure, u is the velocity, K is the bulk modulus, and \(\rho\) is the density.

The initial condition is a Gaussian and the boundary conditions are periodic. The final solution is identical to the initial data because both waves have crossed the domain exactly once.

Output:

Source:

#!/usr/bin/env python
# encoding: utf-8

r"""
One-dimensional acoustics
=========================

Solve the (linear) acoustics equations:

.. math::
    p_t + K u_x & = 0 \\
    u_t + p_x / \rho & = 0.

Here p is the pressure, u is the velocity, K is the bulk modulus,
and :math:`\rho` is the density.

The initial condition is a Gaussian and the boundary conditions are periodic.
The final solution is identical to the initial data because both waves have
crossed the domain exactly once.
"""
from __future__ import absolute_import
from numpy import sqrt, exp, cos
from clawpack import riemann


def setup(use_petsc=False, kernel_language='Fortran', solver_type='classic',
          outdir='./_output', ptwise=False, weno_order=5,
          time_integrator='SSP104', disable_output=False, output_style=1):

    if use_petsc:
        import clawpack.petclaw as pyclaw
    else:
        from clawpack import pyclaw

    if kernel_language == 'Fortran':
        if ptwise:
            riemann_solver = riemann.acoustics_1D_ptwise
        else:
            riemann_solver = riemann.acoustics_1D

    elif kernel_language == 'Python':
        riemann_solver = riemann.acoustics_1D_py.acoustics_1D

    if solver_type == 'classic':
        solver = pyclaw.ClawSolver1D(riemann_solver)
        solver.limiters = pyclaw.limiters.tvd.MC
    elif solver_type == 'sharpclaw':
        solver = pyclaw.SharpClawSolver1D(riemann_solver)
        solver.weno_order = weno_order
        solver.time_integrator = time_integrator
        if time_integrator == 'SSPLMMk3':
            solver.lmm_steps = 4
    else:
        raise Exception('Unrecognized value of solver_type.')

    solver.kernel_language = kernel_language

    x = pyclaw.Dimension(0.0, 1.0, 100, name='x')
    domain = pyclaw.Domain(x)
    num_eqn = 2
    state = pyclaw.State(domain, num_eqn)

    solver.bc_lower[0] = pyclaw.BC.periodic
    solver.bc_upper[0] = pyclaw.BC.periodic

    rho = 1.0   # Material density
    bulk = 1.0  # Material bulk modulus

    state.problem_data['rho'] = rho
    state.problem_data['bulk'] = bulk
    state.problem_data['zz'] = sqrt(rho*bulk)   # Impedance
    state.problem_data['cc'] = sqrt(bulk/rho)   # Sound speed

    xc = domain.grid.x.centers
    beta = 100
    gamma = 0
    x0 = 0.75
    state.q[0, :] = exp(-beta * (xc-x0)**2) * cos(gamma * (xc - x0))
    state.q[1, :] = 0.0

    solver.dt_initial = domain.grid.delta[0] / state.problem_data['cc'] * 0.1

    claw = pyclaw.Controller()
    claw.solution = pyclaw.Solution(state, domain)
    claw.solver = solver
    claw.outdir = outdir
    claw.output_style = output_style
    if output_style == 1:
        claw.tfinal = 1.0
        claw.num_output_times = 10
    elif output_style == 3:
        claw.nstep = 1
        claw.num_output_times = 1
    claw.keep_copy = True
    if disable_output:
        claw.output_format = None
    claw.setplot = setplot

    return claw


def setplot(plotdata):
    """
    Specify what is to be plotted at each frame.
    Input:  plotdata, an instance of visclaw.data.ClawPlotData.
    Output: a modified version of plotdata.
    """
    plotdata.clearfigures()  # clear any old figures,axes,items data

    # Figure for pressure
    plotfigure = plotdata.new_plotfigure(name='Pressure', figno=1)

    # Set up for axes in this figure:
    plotaxes = plotfigure.new_plotaxes()
    plotaxes.axescmd = 'subplot(211)'
    plotaxes.ylimits = [-0.2, 1.0]
    plotaxes.title = 'Pressure'

    # Set up for item on these axes:
    plotitem = plotaxes.new_plotitem(plot_type='1d_plot')
    plotitem.plot_var = 0
    plotitem.plotstyle = '-o'
    plotitem.color = 'b'
    plotitem.kwargs = {'linewidth': 2, 'markersize': 5}

    # Set up for axes in this figure:
    plotaxes = plotfigure.new_plotaxes()
    plotaxes.axescmd = 'subplot(212)'
    plotaxes.xlimits = 'auto'
    plotaxes.ylimits = [-0.5, 1.1]
    plotaxes.title = 'Velocity'

    # Set up for item on these axes:
    plotitem = plotaxes.new_plotitem(plot_type='1d_plot')
    plotitem.plot_var = 1
    plotitem.plotstyle = '-'
    plotitem.color = 'b'
    plotitem.kwargs = {'linewidth': 3, 'markersize': 5}

    return plotdata


def run_and_plot(**kwargs):
    claw = setup(kwargs)
    claw.run()
    from clawpack.pyclaw import plot
    plot.interactive_plot(setplot=setplot)

if __name__ == "__main__":
    from clawpack.pyclaw.util import run_app_from_main
    output = run_app_from_main(setup, setplot)