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WIP: make plots with red/blue stripes advected with flow #68

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merged 11 commits into from
May 18, 2017
Merged

WIP: make plots with red/blue stripes advected with flow #68

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3d38504
separated out code to compute trajectories and use to plot red/blue s…
rjleveque Apr 23, 2017
ddd8257
fix exact_solvers/traffic_LWR.py to use new trajectories code.
rjleveque Apr 24, 2017
660ed53
New Introduction.ipynb from old Prologue notebooks, with SW stripe ex…
rjleveque Apr 24, 2017
b4b0a19
Minor cleanup of stripe plotting code.
ketch Apr 25, 2017
decc0ef
Add acoustics phase plane demo.
ketch Apr 25, 2017
65f9b99
no reload in Python 3
ketch Apr 25, 2017
e63f58d
change 'time' to 't' and initialize to 0 in Introduction
rjleveque May 1, 2017
345c798
First pass at utils/jsanimate_widgets.py, illustrated in Introduction
rjleveque May 1, 2017
56d97f8
Add a bit to Introduction
rjleveque May 6, 2017
078387d
Merge branch 'master' into plot_red_blue_stripes
rjleveque May 6, 2017
442fde2
Add shallow water javascript to Introduction
rjleveque May 6, 2017
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181 changes: 54 additions & 127 deletions Acoustics.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -2,10 +2,7 @@
"cells": [
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"\n",
"# Riemann problem for acoustics\n",
Expand All @@ -16,11 +13,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
Expand All @@ -30,22 +23,15 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"The next cell imports a module containing a function that takes a Riemann problem (left state, right state, and approximate solver), and computes the Riemann solution, as well as functions to plot the solution in various forms. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"from utils import riemann_tools"
Expand All @@ -54,11 +40,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"from utils import animation_tools\n",
Expand All @@ -69,10 +51,7 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"# Acoustics: exact solution\n",
"We can use this to examine the exact solution of an acoustics Riemann problem.\n",
Expand All @@ -96,11 +75,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"from clawpack.riemann.acoustics_1D_py import acoustics_1D\n",
Expand All @@ -109,22 +84,15 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"### Set some problem data needed by the solver:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"problem_data = {}\n",
Expand All @@ -143,22 +111,15 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"### Set the left and right states, and solve the Riemann problem"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"q_l = np.array((1,4)) # Left state\n",
Expand All @@ -170,22 +131,15 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"### Plot the states in the phase plane:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"fig = plt.figure(figsize=(4,3))\n",
Expand All @@ -195,56 +149,39 @@
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"### Plot the waves in the x-t plane, and the solution at one particular time:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"fig = riemann_tools.plot_riemann(states,s,riemann_eval,t=0.5)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"### Animate the Riemann solution:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"riemann_tools.JSAnimate_plot_riemann(states,s,riemann_eval)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"## Shock tube problem:\n",
"\n",
Expand All @@ -254,11 +191,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"q_l = np.array((5,0)) # Left state\n",
Expand All @@ -275,22 +208,15 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"riemann_tools.JSAnimate_plot_riemann(states,s,riemann_eval)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"### Plot the particle trajectories\n",
"\n",
Expand All @@ -308,22 +234,26 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"riemann_tools.plot_riemann_trajectories(states,s,riemann_eval,i_vel=1)"
"wave_types = ['contact','contact'] # for a linear system of 2 equations\n",
"\n",
"# Specify number of trajectories to left and right:\n",
"num_left = 10\n",
"num_right = 10\n",
"\n",
"# compute trajectories:\n",
"x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(states, s, riemann_eval, wave_types,\n",
" i_vel=1, num_left=num_left, num_right=num_right)\n",
"\n",
"# plot trajectories along with waves in the x-t plane:\n",
"riemann_tools.plot_riemann_trajectories(x_traj, t_traj, s, wave_types)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"## Flow into a wall:\n",
"\n",
Expand All @@ -333,11 +263,7 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"q_l = np.array((3,2)) # Left state\n",
Expand All @@ -354,35 +280,36 @@
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"riemann_tools.JSAnimate_plot_riemann(states,s,riemann_eval)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Again we can plot particle trajectories:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"metadata": {},
"outputs": [],
"source": [
"riemann_tools.plot_riemann_trajectories(states,s,riemann_eval,i_vel=1)"
"# compute trajectories:\n",
"x_traj, t_traj, xmax = riemann_tools.compute_riemann_trajectories(states, s, riemann_eval, wave_types,\n",
" i_vel=1, num_left=num_left, num_right=num_right)\n",
"\n",
"# plot trajectories along with waves in the x-t plane:\n",
"riemann_tools.plot_riemann_trajectories(x_traj, t_traj, s, wave_types)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"metadata": {},
"source": [
"If you discard half the solution (for $x>0$ or for $x<0$) then what you see can be viewed as the solution to a problem with fluid streaming at constant velocity toward a solid wall. The result is an acoustic wave that moves away from the wall, and the fluid behind the shock has been decelerated to velocity 0, i.e. it is stationary at the wall.\n",
"\n",
Expand All @@ -406,9 +333,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
"nbformat_minor": 1
}
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