{ "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 Gamma_law, Gamma_law_react, ReactiveRelFactory" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eos = Gamma_law(5.0/3.0)\n", "f = ReactiveRelFactory()\n", "test_1_U_left = f.state(10.0, 0.0, 0.0, 2.0, eos, label=\"L\")\n", "test_1_U_right = f.state(1.0, 0.0, 0.0, 1.5e-6, eos, label=\"R\")\n", "test_1_rp = f.riemann_problem(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": { "image/png": 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\\\\ 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}$" ], "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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UU+zdu7da59q2bRtt2rSpeEfXvHnzmDt3LosXL2bQoEHExsby9ddfk5SUxFlnncXIkSOJi4urVky1Wcfk+uQW+CL+PtS6nVl0bh6x4+KMH576cjW/7D/EmIt6EBMdnFRiCSpIxowZQ5cuXViwYAFdunRh3rx59OzZk9mzZ9OvXz9mzpzJgAED+Nvf/lat81x33XVMmDDBr32LupX37t2bpKQk/ve//5Gdnc0JJ5yAqvLkk09Sv75dsqmOokteabuyQhxJ8BQU+tiwK5tOza2u1FYLNmTyzvzNXH9Se05snxS081j7PEhEhHfeeYchQ4aQkpLCvHnzGD58OK+//vqRe1Djxo3jz3/+M7fddluV5/D66quv6NSpEx06dKhw33fffZfc3Fzmzp1L8+bN6dWrFwcPHmTFihVMmzaNFi1aVCkG86tOyU6rYtX2LE7vGtwZ7ENlw+5s8gp9dLEWVMDtzc5jY2Y2zlBJ5zKxatEjKBpCqaq/2XbkWYl9tdQyfj2Wkvv8WsyR8Zpa7LygqMLYL1fTNimB+84JfMeI4ixBBVGdOnX4/PPP6d+/P5dddhkvvvgi9957L2PGjOH//u//eP7557n44osZPXo0EydOrNI5nn76ae6///4KE9TBgwcZNWoUycnJ9OrViwMHDrBq1SoKCgoYP348xx9/vHWKCIBGCbG0a5LA8vT9oQ4laJZu3QdArxTr5RlI6XtzuOCleezJzgt1KBWKiRLeu2EACXHBTSGWoIIsOTmZadOmMWTIEK699lrGjx/P2WeffWRK/rZt2/LCCy+wbNkyevXqVeny/e0kMXbsWNq2bcuOHTvYutWZkLlhw4ZceeWVXHjhhWE/GNdLeqU0ZvGmyF0Pc2n6PhrEx9Chab1QhxIxDucXcst7P5Jf4GP81X1IiIs+8oVRgKLvjoIUe1z0n1K241zFKb7t1++fJbeXfx5K2Z5UL47mDesE4J2Xzz6VasBxxx3H+++/z9VXX83pp5/Opk2b2LlzJxdccAEvv/wyV199NampqXzxxReVasWoKlu3bq2wk8SmTZt4+eWXiYqKol69ejRt2pSYmBjat2/PfffdR506wa9otcnxKY34fOkv7MrKpVmDwHe9DbVl6fvp0boRUeG3xMZviMhQ4HkgGmdm87ElXo/HWeSyL5AJXKGqm4IRy9PT17B8234mXNuXs4+zS+1FrJNEDTnnnHMYM2YM33//PdnZ2fTv358333yToUOHkp6ezpIlS5g1a1alylRVpkyZQr165X+TTU1NpW3btrRo0YKEhATy8vLIy8vjxRdfDNoiioEmIlEiEhZfqIoufRVdCoskuQWFrNp+gOPDfFHGYivqngt0B64Uke4ldhsJ7FXVjsA44KlgxDJn7S7enLuREYPaWXIqIawTlIgEp/N9kNxyyy1cfPHF5Ofn89VXX3H22WezZs0aFi9ezAUXXFDpKZBycnIqnOLo22+/5ZtvvmHLli2kp6ezfft29u3bx2uvvUa4LE0tIrcBO4HNIrJURG4IdUzl6ZXSiLiYKBZsyAx1KAG3PH0/+YVaY6sGi8h3InJaEIo+sqKuquYBRSvqFnch8Lb7+BPgDAnwjdp9OXnc+/FSOiXX58Hfdwtk0REhrBMU8GnJDe5yCZ717LPPkpKSQqdOnZgxYwY+n49BgwYxffp09u3bx0cffeR3WTNnzuTmm28u8/WibuXR0dHExsYSExNDTEwMf/3rXznllFPCaWXce4CeqtoaGAqcLCKPhjakstWJjaZfu0Tmpu0OdSgB9936TERgYIfgdS0u4SbgNhH5WkQGBbDcslZRLnUfd/bz/TiLGP6GiNwkIotEZNGuXeUvdV7SU1+uJjM7j3FX9KZOrA2OLylsPqGKE5HLRWQs0EBEurnN9SL+DQoKkaioKD788EMOHDjAcccdx6FDh/j6669JSUmhe/fu/OUvf/F7CqSKOki8/fbb7Nq1i6ioKOLi4oiPj+fiiy/muuuuC7fBuAeBDAB3naaRwCUhjagCJ3dsyuodWew+WP3prLzku/W76d6yIY0Taqb+qOrPqnopcB/wkIhMFZHeASi6tJZQyek//NkHVZ2gqv1UtV+zZs38DmDRpj188MNW/t/J7QO6REUkCcsEBcwDVgKJwLPAOhH5UUSmAp4fwl+/fn2mTZvGunXriIuLo2vXrvzyyy/MmTOH+vXrM378eL/KKS9BZWVlkZqaSmZmJgcOHCAnJ4eUlBT++te/huNg3FeAj0Wko/u8LeDpNS1O7tgUgLnrIqcVdTi/kB837+OkY49qRNSENGAMTktnUQDK82cV5SP7uPc/GwEB6Z5ZUOjjoU9/plWjOtx5ZmCXqIgkYZmgVHWbqr4DXKiq56pqB+BM4BHg9NBG55+UlBQ+//xztmzZwsaNG2nYsCFdu3bF5/MxduxY9u2r+Ab7gAEDGDx4cKmvPfnkkwBER0dTUFBAdHQ0EyZMoHnz8Bs8qqrjgfeBN0RkD86H1RoRGSYilV8Iqwb0bN2IZg3imb5iR6hDCZjvN+4hr9DHScc2rbFzisgsEdkKLAYeBPYSmIUDK1xR131+nfv4MmCWBmi10X//mM6anVk8fF53m8+wHGGZoIqo6rxij/eo6mJVDZu1Dvr27ctbb71Fbm4uGzduZN26dWRnZ9OiRQvGjh1b4fHDhg1jwIABR23fuHEjL774IocOHUJEiI6OZvz48fTo0SNsB+Oq6mRVPRVIBvoAs4CTgNdCGVdZoqOEc3u04Js1GeTkFYQ6nICYsXIHCXHRDKrZFtS9QGdV7aSqF6rqKFV9r7qF+rmi7ptAExFJA+4GHqjueQEO5RUybsY6TmjbmKE9rNdeecI6QUWCiy66iAcffJC6desSFRXFgQMH2LJlC6+++uqRAbVl6devHxkZGUdtv+uuuygsLCQ/Px9V5a677uL888+PiMG4qlqgqstU9W1VvUtVPdtiPrdHSw7n+5i1+ui/Ubjx+ZQZK3cypHOzGr2Zr6o/qmpQLtur6heq2llVj1XVJ9xto1V1ivv4sKoOU9WOqtpfVTcE4rwTv9vEjgOHSR3aNWy/MNYUS1AecPfddx9JIAkJCSQmJtKsWTNGjx5d5jF5eXksW7aMJk1++212zpw5R3oHqiqnnHIK99xzjw3GDYH+xyTRomEdPl6UHupQqm3Ztv3sPJDL2ceF3yViLzmUV8jr325gSOdmDOwQknt5YcUSlAeICK+88gpdunQhOzubffv2kZGRwSeffMLy5ctLPWbbtm20bNnyN+s2FRYWcuONN5KXl4fP56N58+aMHz++1q+MKyJDRWSNiKSJyFGXaUTkehHZJSJL3J+AjLOKjhKuOLENc9btYkump/t0VOg/S7YRFx3F6V0sQVXHx4u3sic7j1tP61jxzsYSlFfExMTw2WefkZiYyKFDh8jPzycmJobU1NQjswoXl5WVdVQHiTfffJONGzeiqsTExPDOO+/Qrl1YjWUOOD9nDAD4UFV7uz9vBOr8w/u3QYD3f9gcqCJrXF6Bj89+2sZZ3ZvTKCE21OGErYJCH69/u4ET2jbmxPbhMYNLqFmC8pBGjRoxY8YM6tSpQ2FhIT6fj2+//ZbZs2cftW+vXr149913jzzPysrinnvuoaCgABHhmWee4aSTTgqnwbjB4s+MAUHTslFdhvZowfsLtrA/J7+mThtQX6/ayd6cfC7rlxLqUMLaVyt3snXPIW4efKzde/JTrf/08ppjjjmGqVOnIiLk5uaSm5vLnXfeedQUSJMnT2batGlHnt9///0cPHgQgMsvvzwcB+MGiz8zBgBcKiLLROQTESlz9t2qzBrw59M7cTC3gDfnbaxU4F7x/vdbaNGwDoM7+T8I1RztX99voXXjupzV3S6T+ssSlAedfPLJvPHGG6gqhYWFrF279qgpkL766is2b3YuG23YsOHIqrodO3bkueeeC8fBuMHiz2wAnwPtVbUXMJNf5187+sAqzBrQrWVDhh7Xgn/O3Rh2M0us+GU/c9N2c91J7YkO89nLQ2lLZg5z03Zzeb829nushPDvdxyhrrnmGpYvX84zzzxDXl4ed911F5dccgnx8c7yDVu2bOG8884D4LLLLsPn8xEfH8+///1vmjatuYGUYaDCGQNUtfisrq8ThFmr7z2nC1+v3slT/13N08OOD3TxpUrLyGLtzoNHVlYtWlVVVX+7raztwBfLt1MvLpqrBlRtxWfj+HDRFqIELj/RLpNWhiUoDxs7dixLly5l+vTpZGRk8OyzzzJq1CgAtm7dStu2bZk2bRo//fQTABMnTqRbt252ffu3jswYAGzDmTHgquI7iEhLd44/gAtwBm4GVMfk+vy/U47htf9t4IoT29CvffAnW73xncVs3F39ces3D+lAo7rWOaKqfD5l8o/bGNK5GS0b1Q11OGHFEpSHiQhTpkyhS5cubNq0iUcffZRbbrmFxo0bM2/ePOLj4xk0yJng+cYbb+Siiy6KiMG4gaSqBe5yHdNxFqZ7q2jGAGCROyjzdnf2gAKcudauD0Yst5/eiWnLtnP3R0uZdvspNKgT3A/9w/mFnN29Ofec3QWR4iumClHirrjqbvvNiqzua1ECUSIkR9iiiyKSBHwItAc2AZer6t5S9isEisZ5bFHVC0ru44+ftu5l+35nYK6pHPs087i4uDgWLlxISkoKubm53HLLLbz55pt88803TJ8+nZycHDp06MDTTz9tg3HLoKpfAF+U2Da62ONRwKhgx1EvPobnh/dm2Kvzefiznxl3Re+gt3YbJ8TSpUWDoJ4jDD0AfK2qY91xcQ8AqaXsd0hVqz1z+tRl24mLieKMbsnVLarWqZUJqqKlnr2madOmfP/99/Tu3ZtJkyZx3XXXkZqaypo1a4iOjmbGjBk0amTT9YeDvu2SuPPMzjw7Yy0dk+tzWtfgfWjlF/qCVnaYuxA41X38NjCb0hNUpR3KL2TJ1n0UFPoo8CmFPuW/y3cwpHOzoLeYI1GtS1DFBm6ehXMDfaGITFHVlaGNrHzHH388EyZM4KabbmL48OHk5DgzE0yaNClsVsY1jttO68jP2/bzzFdreeartUE9V11bBK80zYvuOarqdhEp61tCHRFZhHPpd6yqflZRwWkZB7no5XlHbX/oeFsttypqXYKi2MBNABEpGrjp6QQFzn2mSZMmMWvWLAB+//vfc8EFF9hg3DATFSW8dFUf5q3fTV5B8Fo5gjMfYG0kIjOB0qYKf6gSxbRV1V9EpAMwS0SWq+r6Us51E87KvzRPac8/rz+R6CghJkqIiY4iIS6a41o1rNL7qO0kQMubhA0RuQwYqqo3uM+vBQao6m0l9jtS6YAewM/FXvZCW70ZULn1pQOngFJWFgW6qGqtueEhIruAbMBLqxI2xTvxFMXSTlU9M8pXRNYAp7qtp5bAbFXtUsExE4GpqvpJBfvtAjbjzb+DF1SqTtTGFpTfyzjjLh8vIotUtV+wA6sMr8YU6hhqkqo289rfwUvxeCmWEooWIhzr/v8/JXcQkUQgR1VzRaQpcDLw94oKLvrQ9dJ7D+dYauO1IX+WejbGRK6xwFkisg7nXvRYABHpJyJFEwV3AxaJyFLgG5x7UJ6/DRBpamMLqsKBm8aYyOXOHHJGKdsXATe4j78DetZwaKaEWpegyhq4WcFhE4IfWaVZTN7gtffspXi8FEtN89J7D9tYal0nCWOMMeGhNt6DMsYYEwYsQRljjPEkS1B+EpFhIrJCRHwiEtIumyIyVETWiEiaO5dYSInIWyKSISI/V7x35PFC3fBSnajt9aGI1YvfxFGlOmEJyn8/A5cAc0IZRLGpms4FugNXikj3UMYETASGhjiGUApp3fBgnZhI7a4PRaxe/GoiVagTlqD8pKqrVHVNqOOg2FRNqpoHFE3VFDKqOgdnmYpayQN1w1N1orbXhyJWL35V1TphCSr8tAa2Fnue7m4ztZfVCVOasK8XtW4cVHnKm2BSVY+aDiVE/JqqyQSWx+uG1YkQsXoRXJagilHVM0Mdgx9sqqYQ8HjdsDoRIlYvgssu8YWfI1M1iUgczlRNU0IckwktqxOmNGFfLyxB+UlELhaRdGAQME1EpociDlUtAIqmaloFfOTHVE1BJSIfAPPhcO0gAAAgAElEQVSBLiKSLiIjQxlPTQt13fBanajt9aGI1YtfVbVO2FRHxhhjPMlaUMYYYzzJEpQxxhhPsgRljDHGkyxBGWOM8SRLUMYYYzzJEpQxxhhPsgRljDHGkyxBhRkR+UZEznIf/1VEXgh1TCb0RGSIu95OoYhsFJF7Qh2TCa1IqBM2F1/4eQR4XESSgROAC0Icj/GG5sDHOJOU7gt1MMYTwr5OWAsqzLjrqghwNzBcVQtDHJLxhuuAmcD+UAdiPCPs64QlqDAjIj2BlkCuqmaFOh7jGS8C7wL7ROSqUAdjPCHs64QlqDAiIi2B93FWxcwWkXNCHJLxABHpCvwdOB9orKr/CnFIJsQipU7YZLFhQkQSgK+B0ao6Q0QGA0+p6qAQh2ZCTETGAUtVdWKoYzHeECl1wjpJhAlVzcGZtr/o+Zziz02tVofSV3U1tVdE1AlrQRkT5kSkA/A6Tq+t7cAIVd0e2qhMKEVKnbB7UMaEOVXdoKpnqGoPnCW9+4Q6JhNakVInLEEZEyFE5DygHk7XYmPCvk7YJT5jjDGeZC0oY4wxnmQJyhhjjCdZgjLGGONJlqCMMcZ4kiUoY4wxnmQJyhhjjCdZgjLGGONJlqCMMcZ4kiUoY4wxnmQJyhhjjCdZgjLGGONJnkhQIjJURNaISJqIPFDK6/Ei8qH7+vci0r7Ya6Pc7WuKrzBbVpkiMlFENorIEvend7DfnzHGmMoL+YKFIhINvAycBaQDC0VkiqquLLbbSGCvqnYUkeHAU8AVItIdGA4cB7QCZopIZ/eY8sq8T1U/CfqbM8YYU2VeaEH1B9Lc9UvygEnAhSX2uRB42338CXCGiIi7fZKq5qrqRiDNLc+fMo05QkTaiMg3IrJKRFaIyB2hjsmY2s4LCao1sLXY83R3W6n7qGoBsB9oUs6xFZX5hIgsE5FxIhIfiDdhwl4BcI+qdgMGAre6LXRjTIiE/BIfIKVsK7lIVVn7lLW9tMRbVOYoYAcQB0wAUoHHjwpK5CbgJoB69er17dq1a2mxm2IWL168W1WbhTqOqnCXw97uPs4SkVU4X2pWlnVMo8Qkbd6qDSIAggjUiY0mJqq0ahl5FMg6lI+vgiXl1q9aFrb1orIaFtUJ97kIRIlQL94LH7Xe4e9nhRd+a+lAm2LPU3CWKC5tn3QRiQEaAXsqOLbU7e4HEUCuiPwTuLe0oFR1Ak4Co1+/frpo0aLKvataSEQ2hzqGQHA74ZwAfF/Ka0e+uMS16Eje+U/+5vW+HZvw/g0Dgx+kB0xd9gu3/eunindcdV5E1At/5NZpQn6JOgHw2v/rz+DOtSJH+8XfzwovJKiFQCcROQbYhtPp4aoS+0wBrgPmA5cBs1RVRWQK8C8ReRank0Qn4AecllWpZYpIS1Xd7t7Dugj4Odhv0IQPEakP/Bu4U1UPlHy9+BeXHsf30Q9vP4VCn5JfqLwyO41l6ftrOOLQWbAhk3px0fzntlPcVmTpOj5VczGFWufmDfjkzsEU+hSfKruycvnjxIWk7z0U6tDCUsgTlKoWiMhtwHQgGnhLVVeIyOPAIlWdArwJvCsiaTgtp+HusStE5COcyzAFwK2qWghQWpnuKd8XkWY4SWwJ8Keaeq/G20QkFic5va+qkyvav05sFMe1anTkee82jZm5KoNDeYXUjYsOYqTe8MPGPfRpl0jH5PqhDsUz4mOi6NKiwZHneQU+AHZl5YYqpLAW8gQFoKpfAF+U2Da62OPDwLAyjn0CeMKfMt3tp1c3XhN53Bb1m8AqVX22KmW0bVIPgC17cn7zIRWJduw/zNqdB7m0T0qoQ/G0uJgokurFsevg4VCHEpa80IvPGC84GbgWOL3YIO7fV6aAdkkJAGzOzA5CeN4yZ+0uAIZ0sfsqFWlWP95aUFXkiRaUMaGmqnMpvVeo39q6CWrLnpxAhORp/1u3i+YN4+nSPLJbioHQrIElqKqyFpQxAdI4IZYGdWLYFOEtqIJCH3PX7WZwp2ZIeb0jDOAmqIOWoKrCEpQxASIidEquz9qdB0MdSlAt2LCH/YfyOaNbcqhDCQvNGsSTcSAX1QoGjJmjWIIyJoC6tmzImh1ZEf1hNG35L9SLi+bULuGboETkLRHJEJFSh5mI4wV3sullItKnqudq2agOuQU+9mTnVT3gWsoSlDEB1LVFA/YfymfHgcjstZVf6OPLn3dwZvfm1IkN6670E4Gh5bx+Ls64yk44A7NfqeqJ2iTWnnuTgWYJypgA6tqiIQCrd2SFOJLgmJu2m705+fyhZ8tQh1ItqjoHZ0xlWS4E3lHHAqCxiFTpTbdt4iSorTZYt9IsQRkTQEW92lZvj8wENemHLTSpFxfWl/f85M8k1oAz/ZWILBKRRbt27Trq9ZTEugBstRZUpVmCMiaAGiXEkpJYl+Xb9oU6lIDLOHCYmasyuKxvCnExEf/R4c8k1s5G1Qmq2k9V+zVrdvS4sIS4GJrWj2dLpiWoyor4WmZMTevbLpHFm/dGXEeJjxZtpdCnDO/fNtSh1AR/JrH2W9ukumzeE9nDD4LBEpQxAda3XSI7D+Tyy/7I6SiRW1DIuws2c0rHphzTtF6ow6kJU4ARbm++gcD+YishVFpHd/hBpH1pCTZPJCgRGSoia9wunQ+U8nq8iHzovv69uxxC0Wuj3O1rROScisoUkWPcMta5ZcYF+/2Z2qVP20QAFm/eG+JIAufTH7ex80AuNw/pEOpQAkJEPsBZHaGLiKSLyEgR+ZOIFE0e/QWwAWeV7teB/6vO+bq2aMie7DwbsFtJlUpQInJ3scddAhGAiEQDL+N06+wOXFnKSqYjgb2q2hEYBzzlHtsdZ2bz43C6jI4XkegKynwKGKeqnYC9btnGBEzXFg1IiItm4cbyOomFj0Kf8tqcDfRs3YhTOjYNdTgBoapXqmpLVY1V1RRVfVNVX1XVV93XVVVvVdVjVbWnqlZrQbiuLZ3OM2sitHdnsPg1F5+INMZJDF1F5DCwDOeD/Y8BiKE/kKaqG9xzTcLp4ll8JdMLgUfdx58AL7mzT18ITFLVXGCjuxxHf3e/o8p0V0k9nV/Xm3rbLbfcMQ4bdmVzxWvzq/MeTQ0RkfmqOqjY8wZAR1X1Y2W9wIiJjmLAMUl8u+7oHl3h6POlv7Bxdzbjr+7jmamNRORcnH+7jYGlOF86PfuP9Mjwg+1Z/K5TZE+w+/Z3m5i6rMq3636jwhaUiHwHnKCqf8SpEN/jDF6rcL0cP/nTnfPIPqpaAOwHmpRzbFnbmwD73DLKOhfw266j+fn5VXhbJkTiAdxFLFHVLGB8TQcxpHMzNmXmhP3M5ofzC3l6+hp6tG7I0ONahDqc4sYDdwMDcRaQfFpErgxtSGVLqhdHi4Z1WL4t8he0fGveRjZn5hAbHVXmj7/8aUHdBDwmIn8B/qKqi4HFVYy9NP505yxrn7K2l/YbKG//ozeWWPL9w5sHlbabKeYjbyz9KCKSDFwjIveoc1e6bk0HMaRLMny+kjlrd3HtoNB0Ksgr8LEvJw8FVEHdqu48BlWl6J590eu/eQ34z5Jf2LbvEE9f1ouoKG+0nlw7VXWe+3imiMzH+fL8QQhjKlff9oks2hQZl33Lsj8nn82ZOdx3ThduPa1jmft9cJN/5VWYoFT1Z+BSdy6qx90m/l9UdYl/p6iQP905i/ZJF5EYoBHOKPDyji1t+26cEeExbiuqWl1HjSeNAuYC/wLGichaQtAZqH2TBNomJTBrdQbXDmpf06cH4PLX5rNka/XHY53apRknee/e0yYR+SvwuKrmAfmAp2/wnNgukWnLtpO+N4cUd/qjSPPjVqdj0AltGwekvMqsB5UGjMG577SokseWZyHQSUSOAbbhdHq4qsQ+U4DrcHrdXAbMUlUVkSnAv9zLOa1wLj3+gNNSOqpM95hv3DImuWX+J0Dvw3iAqn4JdAYQkUE4KzHXeEcYEWFojxb8c95G9uXk0Tih5juL7jxwmD5tG3NJnxREQBD3/xx5zpHn8uv2YvtGRwmneXPWCAUuAW4UkXVAW+B9EemkqutCG1rpTjwmCYCFm/ZEboLavJfoKOH4lBpKUCIyC+eD/zBOx4WVwPUBOTvOPSURuQ2YDkQDb6nqChF5HFikqlNwluJ+1+0EsQcn4eDu95EbUwFwq6oWunEfVaZ7ylRgkvvt6ye3bBOB3JvmIbtxfn6vVkyYs4HpK3ZwxYmhGdzaMbk+1wxsF5JzB5OqXgkgInWAHsDx7s8bItJBVduUd3wodG3RkMSEWP63ZhcXn5AS6nCCYvHmvXRr2YB68YFpv/hTyr3AKlUN2kyHqvoFzriD4ttGF3t8GOebcGnHPgE84U+Z7vYN/NrTz5ig6dG6Ie2bJPD50u0hS1CRzv1sWOT+eFp0lHB61+bMWLmD/EJfpToLhIOcvAIWbd7LtQH8QlThb0hVfwxmcjImUokIF/Ruzbz1u22iUAPAWd2bc+BwAT9EyBi54r5LyySvwMfpXQN3STiyUrgxHnPFiW0Q4IMftoQ6FFOCHzPYXC8iu0RkiftzQ3XPObhzU+rFRTP5x23VLcpzZq3JoF5cNP3aJwasTEtQxgRR68Z1OaNbcz5cuJXcgsJQh2Ncfs5gA/ChqvZ2f96o7nkT4mK4oHdrpi3/hf2HImd8ZV6Bj/8u386pXZOJjwncQpaWoIwJsmsHtiMzO4//LLERDR5yZAYbt5t60Qw2QXdV/7Yczvfx8aKtFe8cJmatzmBvTj6X9Qls5w9LUMYE2e86NeW4Vg15+Zs0Cgp9oQ7HOPxdkPBSEVkmIp+ISKk9AytasLCknimNGNShCa/N2cDh/MhoVU9auIVmDeL5XafAjpezBGVMkIkIt5/Ric2ZOUxZaq0oj/BnVpnPgfaq2guYiTN359EHVbBgYWnuOqszu7JymfjdpkqE7E2rth9g9ppdjBjYjpgA90y0BGVMDTirW3O6tWzIczPX2b0ob6hwBhtVzXQnogZnyY2+gTp5/2OSOLNbMs/PXBf2PTxfmpVGvbhoRgRhxhRLUMbUgKgo4cHfd2XLnhzenLsx1OGYYjPYuGvCDceZseYIEWlZ7OkFwKpABvD4hT2IErjvk6Vhe+l3/vpMpi3fzo2DO9AoITbg5VuCMqaG/K5TM87s1pyXZqWx80DkrLYbjty5OItmm1kFfFQ0g42IXODudruIrBCRpcDtBHAGHYBWjevy2IU9WLBhD099uTqQRdeInLwCHvpsOSmJdfnTkGODcg5LUMbUoIfP60aBT3no059t+e8QU9UvVLWzuyjhE+620e70aqjqKFU9TlWPV9XTVDXgWeSyvimMGNSO17/dyCuz1we6+KBRVR7+bAUbd2fz90t7USc2cF3LiwtpghKRJBGZ4S6/PkNESh3hJSLXufusE5Hrim3vKyLL3YF2L7iLGJZZroicKiL7iw28G13a+UztIyJviUiGiPwczPO0a1KP+8/pwsxVO/l3BA7WNJX3yPnHcWHvVjz15Wqemb4Gny8wX1xUFZ/P+Sn0KQWFPgoKfeQX+sgrcH5yCwo5nP/bn0N5heTkFZCTV0B2bgEH3Z+sw/kccH+em7mOf/+Yzu2ndwrqTPeBmpG8qh4AvlbVse5I7gdwJnM9QkSSgEeAfji9bBaLyBRV3YuzEu5NwAKcefeGAv+toNxvVfW84L81E2YmAi8B7wT7RH88+Ri+WrGT+z9Zyuj/BC8f5uQVEuWRFXBN2aKjhH8MO546MdG89E0ar3+7gaI/W9H6XM6To9f0ch5rscc1F/ewvinceWanoJ4j1AnqQuBU9/HbwGxKJCjgHGCGqu4BEJEZwFARmQ00LFrmWUTeAS7CSVD+lGvMEao6R0Ta18S5oqOEl646gXfmbw5qjz4R4aLepS4YbTwmJjqKsZf2ZECHJFbvcJa1kiP/cZdGgSPLpfz6+OjtiFS4T1EClGJfYMrbt/h2gMYJcVzUu9Vvjg+GUCeo5qq6HUBVt7sroZZU3rLu6aVsr6jcQe5Nz1+Ae4stw2FMhUTkJpxWO23bVn2G8uSGdbj3nC6BCstEABHhkgDPxBDugp6gRGQm0KKUlx7yt4hStlVq+fZifgTaqepBEfk98BnOWldHn7TYBxFwUETWAE1xVuX1Ai/GEnkLD5WgqhOACQDuRKLZeOfvAFYvQmrx4sW7RWQz3vw7eEGl6kTQE5SqnlnWayKyU0Rauq2clkBGKbul8+vlOnAG1M12t6eU2F400K7UclX1QLG4vhCR8SLSVFWP+uMV/yAqFu8iVe1X9rutORZL6KlqM6+9dy/F46VYaoqqNgNvvfdwjiXU3cyLlnKHspdfnw6cLSKJbm+8s4Hp7iW8LBEZ6PbeG1Hs+FLLFZEWxXr69cd5/5mBf1vGGGOqK9QJaixwloisA85ynyMi/UTkDQC3c8QYnJHfC4HHizpMALcAbwBpwHqcDhJllgtcBvzs3oN6ARiuNhjFACLyAc7y8F1EJF1ERoY6JmNqu5B2klDVTOCMUrYvAm4o9vwt4K0y9utRiXJfwulKXFUTKt6lxlgsAaSqV1bxUK+9dy/F46VYapqX3nvYxiLWgDDGGONFob7EZ4wxxpTKElQliMgwd/JIn4iErFeMiAwVkTXuFE8PhDCOGpkeyOu8UC+8UifcWKxeYPWiRBxVqhOWoCrnZ+ASYE6oAhCRaOBl4FygO3CliHQPUTgTcaaXqu1CWi88VifA6kURqxe/mkgV6oQlqEpQ1VWquibEYfQH0lR1g6rmAZNwpnaqcao6B9hT4Y4RzgP1wjN1AqxeFLF68auq1glLUOGnrKmfTO1ldcKUJuzrRajn4vOc8qZmUtXSBhLXtKpM8WSqyeP1wupEiFi9CC5LUCWUNzWTR6QDbYo9Lz7FkwkSj9cLqxMhYvUiuOwSX/hZCHQSkWNEJA4YjjO1k6m9rE6Y0oR9vbAEVQkicrGIpAODgGkiMr2mY1DVAuA2nDkKVwEfhWrJEJseyBHqeuGlOgFWL4pYvfhVVeuEzSRhjDHGk6wFZYwxxpMsQRljjPEkS1DGGGM8yRKUMcYYT7IEZYwxxpMsQRljjPEkS1DGGGM8yRJUmBGRIe66KoUislFE7gl1TCb0rF6YkiKhTthcfOGnOfAxzmSU+0IdjPEMqxempLCvE9aCCj/XATOB/aEOxHiK1QtTUtjXCUtQ4edF4F1gn4hcFepgjGdYvTAlhX2dsEt8YUREugJ/B84HZqtNpGiwemGOFil1wiaLDSMiMg5YqqoTQx2L8Q6rF6akSKkTdokvvNSh9NU7Te1m9cKUFBF1wlpQYUREOgCv4/TO2Q6MUNXtoY3KhJrVC1NSpNQJa0GFEVXdoKpnqGoPnKWb+4Q6JhN6Vi9MSZFSJyxBhSEROQ+oh9OF1BjA6oU5WrjXCbvEZ4wxxpOsBWWMMcaTLEEZY4zxJEtQxhhjPMkSlDHGGE+yBGWMMcaTLEEZY4zxJEtQxhhjPMkSlDHGGE+yBGWMMcaTLEEZY4zxJEtQxhhjPMkSlDHGGE+yBGWMMcaTLEEZY4zxJEtQxhhjPCkm1AGEg6QmTbVtu3YIgIAAIuI8ryVUocDnK3efZUt+2q2qzWoopJBr0qSptnHrhQgIgtSmSuGnxYsX15p6UfyzwupE2fytE5ag/JAdl8i+sx//zbaEuGhm3j2EVo3rhiiqmnXpK9+xePPe8ndact7mmonGGw6WUi8u7ZPCPy4/PkQReZOIeLJeiMhQ4HkgGnhDVceWeH0ccJr7NAFIVtXG5ZVZ2mdFfEwUz13Rm3N7tgxY7OHO3zphCcoPrRvX5bGLelBY6KPAp2zOzOHdBZvZtDu71iSotTuy+F2nppzXq+x/ZMOfqsGAPKB147o8euFx5BcqhT4fny/dzg+bMkMdlvGDiEQDLwNnAenAQhGZoqori/ZR1buK7f9n4ISKym3duC6PuXWiwOcjv1CZumw7D366nH7tk2jWID4I7yZyWYLyQ1K9OK4d2O7I89U7DvDugs3szckPYVQ1Jzu3gKzcAk46tilXnNi2zP2G12BMXpBUL44Rg9ofeZ51uIDxs9eTX+gjNtpu73pcfyBNVTcAiMgk4EJgZRn7Xwk8UlGhSfXiuLZYnQA4u3tz/vDCXEZNXsaEa/sRFWXX/Pxl/4qqIDEhDoB9h/JCHEnNyMjKBaB5Q/v2V562SQkU+pRtew+FOhRTsdbA1mLP091tRxGRdsAxwKyqnKhT8wakntuVmasyeOV/66tSRK1lCaoKGtWNBWBfLWlB7dh/GIDmDeuEOBJva9ekHgCb9+SEOBLjh9KaMVrGvsOBT1S1sNSCRG4SkUUismjXrl2lFvD/Tm7Phb1b8cxXa5i+YkfVIq6FLEFVQZ3YaOrGRrMvp7a0oIoSVOS3oEQkWkR+EpGplT22bVICAFsyswMelwm4dKBNsecpwC9l7Dsc+KCsglR1gqr2U9V+zZqV3jFNRPjbJT05PqUxf/7gJ75bv7uqcdcqlqCqKDEhttbcg9peu1pQdwCrqnJgcoN44mOi2JxpLagwsBDoJCLHiEgcThKaUnInEekCJALzq3vChLgY/nn9ibRvksCNby9i0aY91S0y4lmCqqJGCXG1pgWVvjeHRnVjaVAnNtShBJWIpAB/AN6oyvFRUcIxTeuRtutgYAMzAaeqBcBtwHScLyQfqeoKEXlcRC4otuuVwCRVLevyX6Uk1ovj3ZEDaN6wDte++QNz1pZ+SdA4LEFVUWJCbK25B5W+9xApibWiO/1zwP1AmSOSK7rf0K1lQ1ZvzwpiiCZQVPULVe2sqseq6hPuttGqOqXYPo+q6gOBPG/zhnX48OZBtG9aj5FvL+TzpWVdWTSWoKooMSGOvbWmBXWINokJoQ4jqETkPCBDVReXt19F9xu6tGj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LOhchZQKUiwLlol+5mdCoIxERCZLeQYmISJDUoEREJEhqUCIiEiQ1KBERCZIalIiIBEkNSkREgqQGJSIiQVKDShkzuyq/r8oxM/u3mX0+6ZokecqFFMtCJjSLL31mAL8gGkbZmXQxEgzlQoqlPhN6B5U+nwSeBg4mXYgERbmQYqnPhBpU+qwGHgc6zey2pIuRYCgXUiz1mdBHfCliZvOBB4GVwHOuQYqCciEny0omNCw2RczsO8CL7r426VokHMqFFMtKJvQRX7qczuC7d0ptUy6kWCYyoXdQKWJmzcCjRKtz9gOfcPf9yVYlSVMupFhWMqF3UCni7u3ufrW7LyDaunlJ0jVJ8pQLKZaVTKhBpZCZrQDOIFpCKgIoF3KytGdCH/GJiEiQ9A5KRESCpAYlIiJBUoMSEZEgqUGJiEiQ1KBERCRIalAiIhIkNSgREQnS/wFzISG2OuJdNQAAAABJRU5ErkJggg==\n", 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\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{L} = \\begin{pmatrix} 1.0000 \\\\ -0.5000 \\\\ 0.0000 \\\\ 2.0000 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{R} = \\begin{pmatrix} 1.0000 \\\\ 0.5000 \\\\ 0.0000 \\\\ 2.0000 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal C}{\\cal R}_{\\rightarrow}, \\quad p_* = 0.2598, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.8955, -0.5734],\\\\ {\\cal C}: \\lambda^{(1)}= 0.1224,\\\\ {\\cal R}_{\\rightarrow}: \\lambda^{(2)}\\in [0.6019, 0.8202], \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.3748 \\\\ 0.1224 \\\\ 0.0000 \\\\ 1.0397 \\end{pmatrix},\\\\ \\begin{pmatrix} \\rho \\\\ v_x \\\\ v_t \\\\ \\epsilon \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.4478 \\\\ 0.1224 \\\\ 0.0000 \\\\ 1.4504 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eos_air = Gamma_law(1.4)\n", "U_vary_eos_L = f.state(1.0, -0.5, 0.0, 2.0, eos, label=\"L\")\n", "U_vary_eos_R = f.state(1.0, +0.5, 0.0, 2.0, eos_air, label=\"R\")\n", "test_vary_eos_rp = f.riemann_problem(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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\\\\ 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}$" ], "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 = Gamma_law(gamma)\n", "eos_unburnt = Gamma_law_react(gamma, q_unburnt, Cv, t_ignition, eos_burnt)\n", "U_reactive_left = f.state(1, 0, 0, 2, eos_burnt)\n", "U_reactive_right = f.state(10, 0, 0, 3, eos_unburnt)\n", "test_reactive_rp = f.riemann_problem(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)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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 }