{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Step 2: Non-linear Convection\n", "\n", "I began this trek along the 12 steps of Navier stokes with the extremely simple 1-D linear convection equation shown below:\n", "\n", "$$\\frac{\\partial u}{\\partial t} + c \\frac{\\partial u}{\\partial x} = 0$$\n", "\n", "Next, we up the ante and present a new more complex model known as the 1D convection equation (notice the lack of the word linear) :\n", "\n", "$$\\frac{\\partial u}{\\partial t} + u \\frac{\\partial u}{\\partial x} = 0$$\n", "\n", "Now, instead of a constant factor c multiplying we have the solution u doing that instead. Thus this makes our convection equation behave nonlinearly. We shall follow the exact discretization steps outline in **Step 1** with the following result:\n", "\n", "$$\\frac{u_i^{n+1} - u^n_i}{\\Delta t} + u^n_i \\frac{u_{i}^{n} - u^n_{i-1}}{\\Delta t} = 0$$\n", "\n", "Solving for the same unknown value $u_i^{n+1}$:\n", "\n", "$$u_i^{n+1} = u^n_i - u^n_i \\frac{\\Delta t}{\\Delta x}(u_i^n - u^n_{i-1})$$\n", "\n", "The following step is a condensed version of what we did to set up initial conditions, variables and libraries and is taken directly from the previous notebook.\n", "\n", "## Libraries & Initial Conditions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "