{ "cells": [ { "cell_type": "markdown", "id": "4c410dec-b7eb-48f6-b0d1-1d77ffcdbf96", "metadata": {}, "source": [ "# Burgers equation" ] }, { "cell_type": "markdown", "id": "c4aad9ed-6a8b-4988-a170-fccec64ca31a", "metadata": {}, "source": [ "The Burgers equation is a fundamental nonlinear partial differential equation that plays a central role in fluid dynamics, nonlinear wave propagation, and traffic flow modeling. Despite its apparent simplicity, it exhibits rich behavior such as shock formation and nonlinear transport, making it a standard benchmark for testing numerical methods.\n", "\n", "In one spatial dimension, the viscous Burgers equation reads\n", "$$\\partial_t u + u \\, \\partial_x u = \\nu \\, \\partial_{xx} u,$$\n", "\n", "where $u(x,t)$ is the scalar velocity field and $\\nu \\ge 0$ is the viscosity coefficient. In the inviscid limit $\\nu \\to 0$, the equation develops discontinuities in finite time, while for $\\nu > 0$ diffusion regularizes the solution.\n", "\n", "In this notebook, we solve the Burgers equation using **Discrete Exterior Calculus (DEC)**. The goal is to demonstrate how DEC can be used to solve nonlinear conservation laws while maintaining geometric consistency, and to compare its behavior with more traditional finite difference–based discretizations." ] }, { "cell_type": "markdown", "id": "0fbf5c4d-8642-472c-9912-7f34ed9d156d", "metadata": {}, "source": [ "## Imports and reference solution on a fine grid" ] }, { "cell_type": "markdown", "id": "91bae6fa-a201-4887-b635-798f85861221", "metadata": {}, "source": [ "We first import the required packages and define a fine space–time grid, which is used to compute a high-resolution reference solution of the one-dimensional viscous Burgers equation in conservative form\n", "$$\n", "\\partial_t u + \\partial_x\\!\\left(\\frac{u^2}{2}\\right) = \\nu\\,\\partial_{xx} u .\n", "$$\n", "\n", "The spatial domain $x \\in [0,L]$ is discretized with spacing $\\Delta x$, and time is discretized with step size $\\Delta t$. The convective term is approximated using a centered finite difference of the flux,\n", "$$\n", "\\left(\\partial_x \\frac{u^2}{2}\\right)_i^n\n", "\\approx\n", "\\frac{(u_{i+1}^n)^2 - (u_{i-1}^n)^2}{4\\Delta x},\n", "$$\n", "while the diffusive term is discretized as\n", "$$\n", "(\\partial_{xx} u)_i^n \\approx\n", "\\frac{u_{i+1}^n - 2u_i^n + u_{i-1}^n}{\\Delta x^2}.\n", "$$\n", "\n", "Time integration is performed using an explicit Euler scheme,\n", "$$u_i^{n+1}=u_i^n-\\Delta t \\left(\\partial_x \\frac{u^2}{2}\\right)_i^n+\\nu\\,\\Delta t\\,(\\partial_{xx} u)_i^n .$$\n", "\n", "This fine-grid finite difference solution is used as a reference for comparison with the DEC-based discretizations introduced later.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "168ef6a6-ee86-46e0-970c-602ec92512a9", "metadata": {}, "outputs": [], "source": [ "import dctkit as dt_\n", "from dctkit import config\n", "import os\n", "from scipy.io import loadmat\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from dctkit.mesh.simplex import SimplicialComplex\n", "from dctkit.mesh import util\n", "from dctkit.dec import cochain as C\n", "from dctkit.dec.flat import flat_DPD as flat_par\n", "from dctkit.dec.flat import flat_dual_upw as flat_upw\n", "from matplotlib import cm\n", "import pygmo as pg\n", "import math\n", "from jax import jit,lax\n", "import time\n", "import jax.numpy as jnp\n", "from functools import partial" ] }, { "cell_type": "code", "execution_count": 2, "id": "1011da18-6648-4bb6-86b5-bff223b9edd4", "metadata": {}, "outputs": [], "source": [ "config()" ] }, { "cell_type": "code", "execution_count": 3, "id": "e06ce522-463d-41a4-8aa2-18f50fa0f326", "metadata": {}, "outputs": [], "source": [ "# SPACE PARAMS\n", "# spatial resolution\n", "dx = 2**4/2**9\n", "L = 2**4 + dx\n", "# Number of spatial grid points\n", "nx = int(math.ceil(L / dx))\n", "\n", "# vector containing spatial points\n", "x = np.linspace(-L/2, L/2, nx)\n", "# circumcenters\n", "x_circ = (x[:-1] + x[1:])/2\n", "\n", "\n", "# initial velocity\n", "u_0 = np.exp(-1 * (x_circ + 0.5 * L/4)**2)\n", "umax = np.max(u_0)\n", "x_max = np.argmax(u_0)" ] }, { "cell_type": "code", "execution_count": 4, "id": "216c5584-6dac-46f5-b59f-d90ca603eafb", "metadata": {}, "outputs": [], "source": [ "# TIME PARAMS\n", "T = 10\n", "# temporal resolution\n", "dt = 10/2**11\n", "# number of temporal grid points\n", "nt = int(math.ceil(T / dt))\n", "\n", "# vector containing time points\n", "t = np.linspace(0, T, nt) \n", "\n", "#Viscosity\n", "nu = 0.005\n", "\n", "nodes_BC = {'left': np.zeros(nt),\n", " 'right': np.zeros(nt)}" ] }, { "cell_type": "code", "execution_count": 5, "id": "c618544c-8133-42bf-851d-da175da6b470", "metadata": {}, "outputs": [], "source": [ "def main_run_FDM(u,x, dt, dx, nu, max_time_iter):\n", " for t in range(max_time_iter):\n", " u[1:-1, t+1] = u[1:-1, t] + dt * (nu * (u[2:, t] - 2 * u[1:-1, t] + u[:-2, t]) / dx**2 \n", " - 0.25 * (u[2:, t]**2 - u[:-2, t]**2) / dx)\n", " return u" ] }, { "cell_type": "code", "execution_count": 6, "id": "f02973a3-c753-4589-9cad-d1edc1ad58db", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Array containing velocity\n", "u = np.zeros([nx-1, nt]) \n", "\n", "# Initial condition\n", "u[:, 0] = u_0\n", "# Boundary condition at x=0\n", "u[0, :] = 0\n", "# Boundary condition at x=xmax\n", "u[-1, :] = 0 \n", "\n", "u = main_run_FDM(u, x,dt, dx, nu, nt-1)\n", "\n", "\n", "plt.pcolormesh(t,x_circ,u)\n", "plt.xlabel('t', fontsize=16)\n", "plt.ylabel('x', fontsize=16)\n", "plt.title(r'$u(x, t)$', fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0931ac62-6553-4971-807c-ea3e10ed73a3", "metadata": {}, "source": [ "## DEC for Burgers with parabolic and upwind method" ] }, { "cell_type": "markdown", "id": "8aa23129-972e-4bc9-8a42-e1cba9d50b4e", "metadata": {}, "source": [ "We now discretize the Burgers equation using **Discrete Exterior Calculus (DEC)** on a one-dimensional simplicial mesh. The scalar field $u(x,t)$ is represented as a dual 0-cochain, while fluxes are represented as primal 1-cochains. The discrete exterior derivative $d$ and the Hodge star $\\star$ are used to construct discrete differential operators.\n", "\n", "The nonlinear convective flux is evaluated using two different DEC-based closures:\n", "- **Parabolic flux**, equivalent to the finite difference method, yielding a centered (second-order) discretization.\n", "- **Upwind flux**, improving stability in advection-dominated regimes.\n", "\n", "Time integration is performed using an explicit scheme, and the resulting DEC solutions are compared against the fine-grid finite difference reference." ] }, { "cell_type": "code", "execution_count": 7, "id": "ca6e107a-451f-419b-b08a-2646b463b9f0", "metadata": {}, "outputs": [], "source": [ "# define simplicial complex\n", "mesh, _ = util.generate_line_mesh(nx, L, x_min=-L/2)\n", "S = util.build_complex_from_mesh(mesh, space_dim=1)\n", "S.get_hodge_star()\n", "S.get_flat_DPD_weights()\n", "S.get_flat_dual_upw_weights()" ] }, { "cell_type": "code", "execution_count": 8, "id": "b0949e17-6fdc-424c-ac24-c2b136f2a1a0", "metadata": {}, "outputs": [], "source": [ "def compute_time_balance(u_t, nu, scheme: str = \"parabolic\"):\n", " u_coch = C.CochainD0(S, u_t)\n", " dissipation = C.scalar_mul(C.star(C.coboundary(u_coch)), nu)\n", " if scheme == \"upwind\":\n", " flat_u = flat_upw(u_coch)\n", " flux = C.scalar_mul(C.square(C.star(flat_u)), -1/2)\n", " elif scheme == \"parabolic\":\n", " u_sq = C.scalar_mul(C.square(u_coch), -1/2)\n", " flux = C.star(flat_par(u_sq))\n", " total_flux = C.add(flux, dissipation)\n", " balance = C.star(C.coboundary(total_flux))\n", " return balance\n", "\n", "\n", "def run(u_0, nodes_BC, num_t_points, nu, step, scheme: str = \"parabolic\"):\n", " \"\"\"Main run to solve Burgers' equation with DEC.\n", "\n", " Args:\n", " scheme: discretization scheme used.\n", " \"\"\"\n", " u = np.zeros((S.num_nodes - 1, num_t_points//step),\n", " dtype=dt_.float_dtype)\n", " # set initial and boundary conditions\n", " u[:, 0] = u_0\n", " u[0, :] = nodes_BC['left'][::step]\n", " u[-1, :] = nodes_BC['right'][::step]\n", " #NOTE: this for loop can easily be optimized with jax.lax.scan\n", " # but we decided to keep it simple for the introductory purpose\n", " # of the notebook\n", " for t in range(num_t_points//step - 1):\n", " u_t = u[:, t]\n", " balance = compute_time_balance(u_t, nu, scheme)\n", " u[1:-1, t+1] = u[1:-1, t] + step*dt*balance.coeffs[1:-1].flatten()\n", " return u" ] }, { "cell_type": "code", "execution_count": 9, "id": "07f063f8-b73a-4f24-a863-504ed5634129", "metadata": {}, "outputs": [], "source": [ "u_dec_par = run(u_0, nodes_BC, nt, nu, 4, \"parabolic\")\n", "u_dec_upw = run(u_0, nodes_BC, nt, nu, 4, \"upwind\")" ] }, { "cell_type": "markdown", "id": "6255d8bc-9893-44df-b6af-317761bda14f", "metadata": {}, "source": [ "## Plots" ] }, { "cell_type": "code", "execution_count": 10, "id": "5a789203-6ec8-40ac-a81d-b09d5dc6ac05", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1, ax = plt.subplots(1, 3, figsize=(20, 5))\n", "\n", "# First plot (FDM) — keep the returned mappable\n", "pcm = ax[0].pcolormesh(\n", " t[::4], x_circ, u[:, ::4],\n", " shading=\"auto\"\n", ")\n", "\n", "# Use the same norm and cmap for the other plots\n", "ax[1].pcolormesh(\n", " t[::4], x_circ, u_dec_par,\n", " shading=\"auto\",\n", " cmap=pcm.cmap,\n", " norm=pcm.norm\n", ")\n", "\n", "ax[2].pcolormesh(\n", " t[::4], x_circ, u_dec_upw,\n", " shading=\"auto\",\n", " cmap=pcm.cmap,\n", " norm=pcm.norm\n", ")\n", "\n", "for i in range(3):\n", " ax[i].set_xlabel('t', fontsize=16)\n", " ax[i].set_ylabel('x', fontsize=16)\n", "\n", "ax[0].set_title(r'FDM (fine complex)', fontsize=16)\n", "ax[1].set_title(r'Parabolic', fontsize=16)\n", "ax[2].set_title(r'Upwind', fontsize=16)\n", "\n", "# One shared colorbar, driven by the FDM plot\n", "cbar = fig1.colorbar(pcm, ax=ax, orientation='vertical')\n", "cbar.set_label('u', fontsize=16)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "973f6673-3ca9-409e-88ae-3ac153fd43c7", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7, 4))\n", "\n", "# True (FDM)\n", "plt.plot(\n", " x_circ,\n", " u[:, ::4][:, -1],\n", " linewidth=2,\n", " label=\"FDM (True)\"\n", ")\n", "\n", "# Parabolic\n", "plt.plot(\n", " x_circ,\n", " u_dec_par[:, -1],\n", " marker=\".\",\n", " linewidth=0.5,\n", " label=\"Parabolic\"\n", ")\n", "\n", "# Upwind\n", "plt.plot(\n", " x_circ,\n", " u_dec_upw[:, -1],\n", " marker=\".\",\n", " linewidth=0.5,\n", " label=\"Upwind\"\n", ")\n", "\n", "plt.xlabel(r\"$x$\", fontsize=14)\n", "plt.ylabel(r\"$u(x, t_{final})$\", fontsize=14)\n", "plt.legend()\n", "plt.grid(True, alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.11" } }, "nbformat": 4, "nbformat_minor": 5 }