{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Riemann Problems\n", "\n", "The code solves Riemann Problems for the relativistic Euler equations\n", "\n", "$$\n", " \\partial_t \\begin{pmatrix} D \\\\ S_x \\\\ S_t \\\\ \\tau \\end{pmatrix} + \\partial_x \\begin{pmatrix} S_x \\\\ S_x v_x + p \\\\ S_t v_x \\\\ (\\tau + p) v_x \\end{pmatrix} = 0.\n", "$$\n", "\n", "For further details on this system of equations, see the [Living Review of Martí and Müller](http://computastrophys.livingreviews.org/Articles/lrca-2015-3/), particularly [section 3.1](http://computastrophys.livingreviews.org/Articles/lrca-2015-3/articlese3.html#x6-190003.1) for the equations and [section 8.5](http://computastrophys.livingreviews.org/Articles/lrca-2015-3/articlese8.html#x11-1150008.5) for the solution of the Riemann Problem.\n", "\n", "The initial data is piecewise constant: two states $w_{L, R}$ are specified, each in terms of $w = (\\rho_0, v_x, v_t, \\epsilon)$, (the specific rest mass density, normal ($x$) and tangential ($t$) velocity components, and the specific internal energy). At $t=0$ the data is set by $w_L$ for $x<0$ and $w_R$ for $x>0$. Each state has associated with it an equation of state (EOS) to close the set of equations: the EOS does not need to be the same for each state.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code\n", "\n", "To set up a Riemann problem, first set up a left and right state. Each state has its own equation of state. Here we use the first test from the [Test Bench section](http://computastrophys.livingreviews.org/Articles/lrca-2015-3/articlese6.html#x9-690006.3) of the [Living Review](http://computastrophys.livingreviews.org/Articles/lrca-2015-3/):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from r3d2 import eos_defns, State, RiemannProblem" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eos = eos_defns.eos_gamma_law(5.0/3.0)\n", "test_1_U_left = State(10.0, 0.0, 0.0, 2.0, eos, label=\"L\")\n", "test_1_U_right = State(1.0, 0.0, 0.0, 1.5e-6, eos, label=\"R\")\n", "test_1_rp = RiemannProblem(test_1_U_left, test_1_U_right)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann Problem will produce output directly in the notebook:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { 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\n", "text/latex": [ "\\begin{equation}\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{L} = \\begin{pmatrix} 10.0000 \\\\ 0.0000 \\\\ 0.0000 \\\\ 2.0000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{R} = \\begin{pmatrix} 1.0000 \\\\ 0.0000 \\\\ 0.0000 \\\\ 0.0000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal C}{\\cal S}_{\\rightarrow}, \\quad p_* = 1.4479, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.7161, 0.1672],\\\\ {\\cal C}: \\lambda^{(1)}= 0.7140,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.8284, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 2.6393 \\\\ 0.7140 \\\\ 0.0000 \\\\ 0.8229 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 5.0708 \\\\ 0.7140 \\\\ 0.0000 \\\\ 0.4283 \\end{pmatrix}. \\end{cases}\\end{equation}" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test_1_rp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This output should be interpreted as follows. First it displays the initial states ${\\bf U}_{L, R}$. It then gives the resulting wave pattern: in this case a left going rarefaction, a contact, and a right going shock. It then gives the pressure $p_*$ in the central states (the pressure and normal velocity do not jump across the contact). Next it gives the speeds of each wave. Finally, it gives the constant states between the left wave and the contact ${\\bf U}_{*_L}$ and between the contact and the right state ${\\bf U}_{*_R}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also display the output graphically in the notebook:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from IPython.display import display_png" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display_png(test_1_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first (top left) plot is the wave pattern in the $(x, t)$ plane. Rarefactions are shaded with thin solid lines. Contacts are dashed lines. Discontinuities such as shocks are thick solid lines.\n", "\n", "All the other plots show a single quantity as a function of space at a fixed time, or equivalently as a function of the characteristic variable $\\xi = x / t$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Changing equation of state\n", "\n", "There is no need for the two states to have the same equation of state. For example:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "\\begin{equation}\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{L} = \\begin{pmatrix} 1.0000 \\\\ -0.5000 \\\\ 0.0000 \\\\ 2.0000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{R} = \\begin{pmatrix} 1.0000 \\\\ 0.5000 \\\\ 0.0000 \\\\ 2.0000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal C}{\\cal R}_{\\rightarrow}, \\quad p_* = 0.2598, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.8955, -0.5734],\\\\ {\\cal C}: \\lambda^{(1)}= 0.1224,\\\\ {\\cal R}_{\\rightarrow}: \\lambda^{(2)}\\in [0.6019, 0.8202], \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.3748 \\\\ 0.1224 \\\\ 0.0000 \\\\ 1.0397 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.4478 \\\\ 0.1224 \\\\ 0.0000 \\\\ 1.4504 \\end{pmatrix}. \\end{cases}\\end{equation}" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eos_air = eos_defns.eos_gamma_law(1.4)\n", "U_vary_eos_L = State(1.0, -0.5, 0.0, 2.0, eos, label=\"L\")\n", "U_vary_eos_R = State(1.0, +0.5, 0.0, 2.0, eos_air, label=\"R\")\n", "test_vary_eos_rp = RiemannProblem(U_vary_eos_L, U_vary_eos_R)\n", "test_vary_eos_rp" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display_png(test_vary_eos_rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reactive problems\n", "\n", "To include a reaction, make the equation of state of at least one of the states be a reactive EOS:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "\\begin{equation}\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}= \\begin{pmatrix} 1.0000 \\\\ 0.0000 \\\\ 0.0000 \\\\ 2.0000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\\\ q \\end{pmatrix}= \\begin{pmatrix} 10.0000 \\\\ 0.0000 \\\\ 0.0000 \\\\ 3.0000 \\\\ 0.1000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal S}_{\\leftarrow}{\\cal C}\\left({\\cal R}_{\\rightarrow}{\\cal CJDF}_{\\rightarrow}\\right) , \\quad p_* = 5.0558, \\quad\\begin{cases} {\\cal S}_{\\leftarrow}: \\lambda^{(0)}= -0.8710,\\\\ {\\cal C}: \\lambda^{(1)}= -0.5305,\\\\ \\left({\\cal R}_{\\rightarrow}{\\cal CJDF}_{\\rightarrow}\\right) : \\lambda^{(2)}\\in [0.2763, 0.6612], \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 2.1685 \\\\ -0.5305 \\\\ 0.0000 \\\\ 3.4972 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 4.3776 \\\\ -0.5305 \\\\ 0.0000 \\\\ 1.7324 \\end{pmatrix}. \\end{cases}\\end{equation}" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q_unburnt = 0.1\n", "gamma = 5/3\n", "Cv = 1.0\n", "t_ignition = 2\n", "eos_burnt = eos_defns.eos_gamma_law(gamma)\n", "eos_unburnt = eos_defns.eos_gamma_law_react(gamma, q_unburnt, Cv, t_ignition, eos_burnt)\n", "U_reactive_left = State(1, 0, 0, 2, eos_burnt)\n", "U_reactive_right = State(10, 0, 0, 3, eos_unburnt)\n", "test_reactive_rp = RiemannProblem(U_reactive_left, U_reactive_right)\n", "test_reactive_rp" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display_png(test_reactive_rp)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }