From 2d98358890ccdf282c26b773928b57c502d99dcc Mon Sep 17 00:00:00 2001 From: Felix Koehler Date: Tue, 9 Apr 2024 16:11:18 +0200 Subject: [PATCH] Simple validation of Burgers against Cole-Hopf --- .../validate_burgers_against_cole_hopf.ipynb | 305 ++++++++++++++++++ 1 file changed, 305 insertions(+) create mode 100644 validation/validate_burgers_against_cole_hopf.ipynb diff --git a/validation/validate_burgers_against_cole_hopf.ipynb b/validation/validate_burgers_against_cole_hopf.ipynb new file mode 100644 index 0000000..499d202 --- /dev/null +++ b/validation/validate_burgers_against_cole_hopf.ipynb @@ -0,0 +1,305 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Validation of Burgers solver against Cole-Hopf transformation\n", + "\n", + "The Burgers equation\n", + "\n", + "$$\n", + "\\frac{\\partial u}{\\partial t} + \\frac{1}{2} \\frac{\\partial u^2}{\\partial x} = \\nu \\frac{\\partial^2 u}{\\partial x^2}\n", + "$$\n", + "\n", + "can also be solved by first solving a heat equation\n", + "\n", + "$$\n", + "\\frac{\\partial v}{\\partial t} = \\nu \\frac{\\partial^2 v}{\\partial x^2}\n", + "$$\n", + "\n", + "and then applying the Cole-Hopf transformation\n", + "\n", + "$$\n", + "u = -2 \\nu \\frac{\\partial}{\\partial x} \\ln v\n", + "$$\n", + "\n", + "This notebook compares the solution of the Burgers equation with the solution of the heat equation followed by the Cole-Hopf transformation." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import exponax as ex" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "burgers_stepper = ex.stepper.Burgers(1, 2 * jnp.pi, 100, 0.01, diffusivity=0.001)\n", + "diffusion_stepper = ex.stepper.Diffusion(1, 2 * jnp.pi, 100, 0.01, diffusivity=0.001)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "grid = ex.make_grid(1, 2 * jnp.pi, 100)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "u_0_heat = 1.5 - (jnp.exp(-10 * (grid - jnp.pi) ** 2) + 0.1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(u_0_heat[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# u_0_burgers = - 2 * burgers_stepper.diffusivity * exponax.spectral_derivative(jnp.log(u_0_heat), L=2 * jnp.pi, order=1)\n", + "u_0_burgers = (\n", + " -2\n", + " * burgers_stepper.diffusivity\n", + " * ex.derivative(jnp.log(u_0_heat), 2 * jnp.pi, order=1)\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(u_0_burgers[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "heat_trj = ex.rollout(diffusion_stepper, 5000, include_init=True)(u_0_heat)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(5001, 1, 100)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "heat_trj.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "burgers_trj_from_heat = (\n", + " -2\n", + " * burgers_stepper.diffusivity\n", + " * jax.vmap(lambda u: ex.derivative(u, 2 * jnp.pi))(jnp.log(heat_trj))\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "burgers_trj = ex.rollout(burgers_stepper, 5000, include_init=True)(u_0_burgers)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(burgers_trj_from_heat[0, 0, :], label=\"from heat u_0\")\n", + "plt.plot(burgers_trj_from_heat[5000, 0, :], label=\"from heat later\")\n", + "plt.plot(burgers_trj[5000, 0, :], label=\"burgers later\")\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "diff_trj = burgers_trj - burgers_trj_from_heat" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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