Merge 1bd079b into 82c8863

examples/mhd_1d/shocktube.py

@@ -0,0 +1,117 @@
+#!/usr/bin/env python
+# encoding: utf-8
+r"""
+Shock-tube problem
+===================================
+
+Solve the one-dimensional ideal MHD equations for inviscid, compressible flow:
+
+.. math::
+    \rho_t + (\rho u_1)_x &= 0 \\
+    (\rho u_i)_t + (\rho u_1 u_i + (p + B^2 / 2) \delta_{i1} - B_1 B_i)_x &= 0 \\
+    E_t + (u_1 (E + p + B^2 / 2) - B_1 (u \cdot B))_x &= 0,
+    (B_i)_t + (u_1 B_i - u_i B_1)_x &= 0.
+
+The fluid is an ideal gas, with pressure given by :math:`p=\rho (\gamma-1)e` where
+e is internal energy.
+
+This script runs a shock-tube problem, cf. https://doi.org/10.1016/j.jcp.2016.10.034.
+"""
+from __future__ import absolute_import
+from clawpack import riemann
+from clawpack.riemann.mhd_1D_constants import num_eqn, density, momentum_1, momentum_2, momentum_3, energy, B_1, B_2, B_3
+
+gamma = 1.4 # Ratio of specific heats
+
+def setup(use_petsc=False, outdir='./_output', solver_type='classic',
+          kernel_language='Fortran', disable_output=False):
+
+    if use_petsc:
+        import clawpack.petclaw as pyclaw
+    else:
+        from clawpack import pyclaw
+
+    if kernel_language =='Python':
+        raise Exception('Not implemented.')
+    elif kernel_language =='Fortran':
+        rs = riemann.mhd_roe_1D
+
+    if solver_type=='sharpclaw':
+        solver = pyclaw.SharpClawSolver1D(rs)
+    elif solver_type=='classic':
+        solver = pyclaw.ClawSolver1D(rs)
+
+    solver.kernel_language = kernel_language
+
+    solver.bc_lower[0] = pyclaw.BC.extrap
+    solver.bc_upper[0] = pyclaw.BC.extrap
+
+    mx = 800
+    x = pyclaw.Dimension(-4.0, 4.0, mx, name='x')
+    domain = pyclaw.Domain([x])
+    state = pyclaw.State(domain, num_eqn)
+
+    state.problem_data['gamma'] = gamma
+    state.problem_data['gamma1'] = gamma - 1.
+
+    x = state.grid.x.centers
+
+    pressure = 1.0
+    B1_l = 1.5; B1_r = 1.5
+    B2_l = 0.5; B2_r = 1.6
+    B3_l = 0.6; B3_r = 0.2
+    state.q[density,    :] = 1.0
+    state.q[momentum_1, :] = 0.0
+    state.q[momentum_2, :] = 0.0
+    state.q[momentum_3, :] = 0.0
+    state.q[B_1,        :] = (x<0.) * B1_l + (x>=0.) * B1_r
+    state.q[B_2,        :] = (x<0.) * B2_l + (x>=0.) * B2_r
+    state.q[B_3,        :] = (x<0.) * B3_l + (x>=0.) * B3_r
+    state.q[energy,     :] = pressure / (gamma - 1.) + 0.5 * (state.q[momentum_1,:]**2 + state.q[momentum_2,:]**2 + state.q[momentum_3,:]**2) / state.q[density,:] + 0.5 * (state.q[B_1,:]**2 + state.q[B_2,:]**2 + state.q[B_3,:]**2)
+
+    claw = pyclaw.Controller()
+    claw.tfinal = 1.0
+    claw.solution = pyclaw.Solution(state, domain)
+    claw.solver = solver
+    claw.num_output_times = 10
+    claw.outdir = outdir
+    claw.setplot = setplot
+    claw.keep_copy = True
+    if disable_output:
+        claw.output_format = None
+
+    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
+
+    plotfigure = plotdata.new_plotfigure(name='', figno=0)
+
+    plotaxes = plotfigure.new_plotaxes()
+    plotaxes.axescmd = 'subplot(211)'
+    plotaxes.title = '$B_2$'
+
+    plotitem = plotaxes.new_plotitem(plot_type='1d')
+    plotitem.plot_var = B_2
+    plotitem.kwargs = {'linewidth': 3}
+
+    plotaxes = plotfigure.new_plotaxes()
+    plotaxes.axescmd = 'subplot(212)'
+    plotaxes.title = '$B_3$'
+
+    plotitem = plotaxes.new_plotitem(plot_type='1d')
+    plotitem.plot_var = B_3
+    plotitem.kwargs = {'linewidth': 3}
+
+    return plotdata
+
+if __name__=="__main__":
+    from clawpack.pyclaw.util import run_app_from_main
+    output = run_app_from_main(setup, setplot)