{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Relativistic shallow water Riemann problem\n", "\n", "The code can be used to solve the Riemann problem for the relativistic shallow water equations,\n", "$$\n", " \\partial_t \\begin{pmatrix} \\Phi W \\\\ \\Phi W^2 u_j \\end{pmatrix} + \\partial_x \\begin{pmatrix} \\Phi W u^i \\\\ \\Phi W^2 u_j u^i + \\tfrac{1}{2} \\Phi^2 \\delta^i_j \\end{pmatrix} = {\\bf 0}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This can also be written\n", "$$\n", " \\partial_t \\begin{pmatrix} D \\\\ S_j \\end{pmatrix} + \\partial_x \\begin{pmatrix} D u^i \\\\ S_j u^i + \\frac{D^2}{2 W^2} \\delta^i_j \\end{pmatrix} = {\\bf 0}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remember that the Lorentz factor $W^{-2} = 1 - u_j u^j$.\n", "\n", "In these equations, we have defined $\\Phi$ to be the geopotential, which is equal to $\\Phi = gh$ in the Newtonian limit (where $g$ is the graviational acceleration and $h$ is the fluid height).\n", "\n", "As in the Riemann problem for the reative relativistic Euler equations, the initial data is piecewise constant. It consists of two states $w_L$ and $w_R$, where $w = (\\Phi, v)$. At $t = 0$, the $w_L$ gives the data for $x < 0$, and $w_R$ the data for $x > 0$. Unlike for the Euler equations, we do not require an equation of state. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code\n", "\n", "To set up the Riemann problem, we first initialise the SWE factory and define the left and right states." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from r3d2 import SWEFactory" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "f = SWEFactory()\n", "\n", "Ul = f.state(0.41, 0)\n", "Ur = f.state(0.01, 0)\n", "\n", "rp = f.riemann_problem(Ul, Ur, t_end=0.3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann problem will produce output directly in the notebook:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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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" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}= \\begin{pmatrix} 0.41 \\\\ 0 \\end{pmatrix},\\\\ \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}= \\begin{pmatrix} 0.01 \\\\ 0 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal S}_{\\rightarrow}, \\quad \\Phi_* = 0.0996, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.6403, 0.3023],\\\\ ,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.5944, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.09964248856213016 \\\\ [0.54433069] \\end{pmatrix},\\\\ \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.09964248856213016 \\\\ 0.5443306893504382 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "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 geopotential $\\Phi_*$ in the central states (the geopotential and 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 ${\\bf U}_{*_R}$.\n", "\n", "We can also display the output graphically in the notebook:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from IPython.display import display_png" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display_png(rp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The top plot shows 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", "The other two plots show the geopotential and velocity as a function of space at the time given by the `t_end` parameter (which is either defined by the user when creating the Riemann problem or defaults to 1), or equivalently as a function of the characteristic variable $\\xi = x/t$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Extreme example\n", "\n", "In this example, the initial data is more extreme, leading to a very relativistic velocity in the star state." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "Ul = f.state(0.9999, 0)\n", "Ur = f.state(0.00001, 0)\n", "\n", "rp_extreme = f.riemann_problem(Ul, Ur, t_end=0.3)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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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", "\n" ], "text/latex": [ "$\\begin{cases} \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}= \\begin{pmatrix} 0.9999 \\\\ 0 \\end{pmatrix},\\\\ \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}= \\begin{pmatrix} 1e-05 \\\\ 0 \\end{pmatrix}, \\end{cases} \\quad \\implies \\quad {\\cal R}_{\\leftarrow}{\\cal S}_{\\rightarrow}, \\quad \\Phi_* = 0.0104, \\quad\\begin{cases} {\\cal R}_{\\leftarrow}: \\lambda^{(0)}\\in [-0.9999, 0.9020],\\\\ ,\\\\ {\\cal S}_{\\rightarrow}: \\lambda^{(2)}= 0.9190, \\end{cases} \\quad \\begin{cases} \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}_{\\star_L} = \\begin{pmatrix} 0.010419553958219592 \\\\ [0.91865383] \\end{pmatrix},\\\\ \\begin{pmatrix} \\Phi \\\\ v \\end{pmatrix}_{\\star_R} = \\begin{pmatrix} 0.010419553958219592 \\\\ 0.9186538307876264 \\end{pmatrix}. \\end{cases}$" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rp_extreme" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n" 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