# 2-dimensional acoustics¶

## Two-dimensional acoustics¶

Solve the (linear) acoustics equations:

$\begin{split}p_t + K (u_x + v_y) & = 0 \\ u_t + p_x / \rho & = 0 \\ v_t + p_y / \rho & = 0.\end{split}$

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

## Source:¶

#!/usr/bin/env python
# encoding: utf-8
r"""
Two-dimensional acoustics
=========================

Solve the (linear) acoustics equations:

.. math::
p_t + K (u_x + v_y) & = 0 \\
u_t + p_x / \rho & = 0 \\
v_t + p_y / \rho & = 0.

Here p is the pressure, (u,v) is the velocity, K is the bulk modulus,
and :math:\rho is the density.
"""
from __future__ import absolute_import
from clawpack import riemann
import numpy as np

def setup(kernel_language='Fortran', use_petsc=False, outdir='./_output',
solver_type='classic', time_integrator='SSP104', ptwise=False,
disable_output=False):
"""
Example python script for solving the 2d acoustics equations.
"""
if use_petsc:
from clawpack import petclaw as pyclaw
else:
from clawpack import pyclaw

if solver_type == 'classic':
if ptwise:
solver = pyclaw.ClawSolver2D(riemann.acoustics_2D_ptwise)
else:
solver = pyclaw.ClawSolver2D(riemann.acoustics_2D)
solver.dimensional_split=True
solver.cfl_max = 0.5
solver.cfl_desired = 0.45
solver.limiters = pyclaw.limiters.tvd.MC
elif solver_type=='sharpclaw':
solver=pyclaw.SharpClawSolver2D(riemann.acoustics_2D)
solver.time_integrator=time_integrator
if solver.time_integrator=='SSP104':
solver.cfl_max = 0.5
solver.cfl_desired = 0.45
elif solver.time_integrator=='SSPLMMk2':
solver.lmm_steps = 3
solver.lim_type = 2
solver.cfl_max = 0.25
solver.cfl_desired = 0.24
else:
raise Exception('CFL desired and CFL max have not been provided for the particular time integrator.')

solver.bc_lower[0]=pyclaw.BC.extrap
solver.bc_upper[0]=pyclaw.BC.extrap
solver.bc_lower[1]=pyclaw.BC.extrap
solver.bc_upper[1]=pyclaw.BC.extrap

mx=100; my=100
x = pyclaw.Dimension(-1.0,1.0,mx,name='x')
y = pyclaw.Dimension(-1.0,1.0,my,name='y')
domain = pyclaw.Domain([x,y])

num_eqn = 3
state = pyclaw.State(domain,num_eqn)

rho  = 1.0  # Material density
bulk = 4.0  # Material bulk modulus
cc = np.sqrt(bulk/rho)  # sound speed
zz = rho*cc             # impedance
state.problem_data['rho']= rho
state.problem_data['bulk']=bulk
state.problem_data['zz']= zz
state.problem_data['cc']=cc

solver.dt_initial=np.min(domain.grid.delta)/state.problem_data['cc']*solver.cfl_desired

qinit(state)

claw = pyclaw.Controller()
claw.keep_copy = True
if disable_output:
claw.output_format = None
claw.solution = pyclaw.Solution(state,domain)
claw.solver = solver
claw.outdir = outdir
claw.num_output_times = 10
claw.tfinal = 0.12
claw.setplot = setplot

return claw

def qinit(state,width=0.2):
X, Y = state.grid.p_centers
r = np.sqrt(X**2 + Y**2)

state.q[0,:,:] = (np.abs(r-0.5)<=width)*(1.+np.cos(np.pi*(r-0.5)/width))
state.q[1,:,:] = 0.
state.q[2,:,:] = 0.

def setplot(plotdata):
"""
Plot output with VisClaw.
This example demonstrates how to plot a 1D projection from 2D data.
"""

from clawpack.visclaw import colormaps

plotdata.clearfigures()  # clear any old figures,axes,items data

# Figure for pressure
plotfigure = plotdata.new_plotfigure(name='Pressure', figno=0)

# Set up for axes in this figure:
plotaxes = plotfigure.new_plotaxes()
plotaxes.title = 'Pressure'
plotaxes.scaled = True      # so aspect ratio is 1

# Set up for item on these axes:
plotitem = plotaxes.new_plotitem(plot_type='2d_pcolor')
plotitem.plot_var = 0
plotitem.pcolor_cmap = colormaps.yellow_red_blue

# Figure for scatter plot
plotfigure = plotdata.new_plotfigure(name='scatter', figno=1)

# Set up for axes in this figure:
plotaxes = plotfigure.new_plotaxes()
plotaxes.title = 'Scatter plot'

# Set up for item on these axes: scatter of 2d data
plotitem = plotaxes.new_plotitem(plot_type='1d_from_2d_data')

def p_vs_r(current_data):
# Return radius of each patch cell and p value in the cell
from pylab import sqrt
x = current_data.x
y = current_data.y
r = sqrt(x**2 + y**2)
q = current_data.q
p = q[0,:,:]
return r,p

plotitem.map_2d_to_1d = p_vs_r
plotitem.plot_var = 0
plotitem.plotstyle = 'ob'

return plotdata

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