{ "cells": [ { "cell_type": "markdown", "id": "49516829", "metadata": {}, "source": [ "# Finite Volume Method 개요" ] }, { "cell_type": "markdown", "id": "0beaca09", "metadata": {}, "source": [ "**강좌**: *기초 전산유체역학*" ] }, { "cell_type": "markdown", "id": "89a854f4", "metadata": {}, "source": [ "## 보존식에 대한 구성\n", "1차원 보존식 (Conservation Law)는 다음과 같다.\n", "\n", "$$\n", "\\frac{\\partial u}{\\partial t} + \\frac{\\partial f}{\\partial x} = 0.\n", "$$\n", "\n", "불연속한 해 $u$ 를 다루기 위해서 Control volume $[t^n, t^{n+1}] \\times [x_L, x_R]$ 에서 적분형 식을 고려한다.\n", "\n", "$$\n", "\\int_{t^n}^{t^{n+1}} \\int_{x_L}^{x_R} \n", "\\left (\\frac{\\partial u}{\\partial t} + \\frac{\\partial f}{\\partial x} \n", "\\right ) dx dt = 0.\n", "$$\n", "\n", "또는 다음과 같은 weak form을 고려하기도 한다.\n", "\n", "$$\n", "\\int_{0}^{\\infty} \\int_{-\\infty}^{\\infty} \n", "\\left (\n", "\\frac{\\partial w}{\\partial t} u + \\frac{\\partial w}{\\partial x} f\n", "\\right )\n", " dx dt = - \\int_{-\\infty}^{\\infty} w(x, 0) u(x, 0) dx\n", "$$\n", "\n", "여기서 $w(x,t)$ 는 smooth test 함수로, 무한한 시간 또는 무한한 공간 경계에서 값이 0 인 임의의 함수이다.\n", "\n", "첫번째 적분형 식에 대해 차분하면 유한체적법 결과를 얻을 수 있다.\n", "\n", "두번째 식을 활용하는 차분법은 유한요소법 또는 불연속 갤러킨 기법 등을 유도할 수 있다.\n", "\n", ":::{figure-md} FVM\n", "

\n", "\n", "FVM\n", ":::\n", "\n", "여기서 격자 $I_i = [x_{i-1/2}, x_{i+1/2}]$, 시간 $t=t^n$ 에서 근사해 $U_i^n$는 다음과 같다.\n", "\n", "$$\n", "U_i^n \\approx \\frac{1}{\\Delta x_i} \\int_{I_i} u(x, t^n) dx,\n", "$$\n", "\n", "여기서 $\\Delta x_i = x_{i+1/2} - x_{i-1/2}$ 이다.\n", "\n", "위 보존식을 공간에 대해 적분하면 다음과 같다.\n", "\n", "$$\n", "\\frac{d}{dt} \\int_{I_i} u(x, t) dx = -( f(u(x_{i+1/2}, t) - f(u(x_{i-1/2}, t))\n", "$$\n", "\n", "$[t^n, t^{n+1}]$ 구간에 대해 시간 적분을 적용하면 다음과 같다.\n", "\n", "$$\n", "\\int_{I_i} u(x, t^{n+1}) dx - \\int_{I_i} u(x, t^n) dx\n", "=\n", "- \\left (\\int_{t^n}^{t^{n+1}} f(u(x_{i+1/2}, t) dt \n", "- \\int_{t^n}^{t^{n+1}} f(u(x_{i-1/2}, t) dt \\right ). \n", "$$\n", "\n", "여기서 Flux에 대한 적분을 다음과 같이 근사화 하면\n", "\n", "$$\n", "F^n_{i+1/2} \\approx \\frac{1}{\\Delta t} \\int_{t^n}^{t^{n+1}} f(u(x_{i+1/2}, t) dt,\n", "$$\n", "\n", "시간 $[t^n, t^{n+1}]$과 격자 $I_i$ 에 대해 적분한 보존식은 다음과 같이 표현할 수 있다.\n", "\n", "$$\n", "U_i^{n+1} = U_i^n - \\frac{\\Delta t}{\\Delta x} \\left (\n", "F^n_{i+1/2} - F^n_{i-1/2}\n", "\\right )\n", "$$\n", "\n", "격자 경계에서는 Riemann Problem을 풀어서 Flux $F_{i+1/2}^n$ 을 계산한다.\n", "\n", "$$\n", "u(\\hat{x}/\\hat{t}) = \\left \\{\n", "\\begin{array}{cc} \n", "u_L & \\hat{x}/\\hat{t} < \\lambda \\\\\n", "u_R & else \n", "\\end{array}\n", "\\right .\n", "$$\n", "\n", "여기서 $\\hat{x}, \\hat{t}$ 는 $t=t^n$ $x=x_{i+1/2}$ 기준 국소적인 시간과 공간 좌표이다. $\\lambda$ 는 Characteristics의 속도이다." ] }, { "cell_type": "code", "execution_count": 1, "id": "2b5071fd", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "code", "execution_count": 2, "id": "ef3642ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, '$\\\\hat{x}$')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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