{
"cells": [
{
"cell_type": "markdown",
"id": "emotional-asbestos",
"metadata": {},
"source": [
"# Linear Wave 방정식"
]
},
{
"cell_type": "markdown",
"id": "suffering-jersey",
"metadata": {},
"source": [
"**강좌**: *기초 전산유체역학*"
]
},
{
"cell_type": "markdown",
"id": "broken-leisure",
"metadata": {},
"source": [
"## 선형 파동 방정식\n",
"1차원 선형 파동 방정식은 다음과 같다.\n",
"\n",
"$$\n",
"\\frac{\\partial u}{\\partial t} + a \\frac{\\partial u}{\\partial x} = 0.\n",
"$$\n",
"\n",
"여기서 상수 $a$ 는 파의 전파속도이다. 다음 초기 조건에 의한 완전해는\n",
"\n",
"$$\n",
"u(x,0) = F(x),~~~-\\infty < x < \\infty\n",
"$$\n",
"\n",
"아래와 같다.\n",
"\n",
"$$\n",
"u(x,t) = F(x-at).\n",
"$$\n",
"\n",
"## 유한차분법\n",
"$n$ 번째 시간 $t^n$, $j$ 번째 격자점 $x_j$ 에서 근사해를 다음과 같이 표현하자.\n",
"\n",
"$$\n",
"u_j^n = u(x_j, t^n).\n",
"$$\n",
"\n",
"### First approach (Central difference)\n",
"시간에 대한 차분은 우선 Euler Explicit 방법을 생각하자.\n",
"\n",
"$$\n",
"\\frac{\\partial u}{\\partial t} \\approx \\frac{u_j^{n+1} - u_{j}^n}{\\Delta t}.\n",
"$$\n",
"\n",
"공간에 대한 차분은 중앙차분을 생각하자.\n",
"\n",
"$$\n",
"a \\frac{\\partial u}{\\partial x} \\approx a \\frac{u_{j+1}^n - u_{j-1}^n}{2 \\Delta x}\n",
"$$\n",
"\n",
"이를 정리하면 다음 기법을 만들 수 있다.\n",
"\n",
"$$\n",
"u_j^{n+1} = u_{j}^n - \\frac{a \\Delta t}{2 \\Delta x} (u_{j+1}^n - u_{j-1}^n).\n",
"$$\n",
"\n",
"### Second approach (Upwind difference)\n",
"$a>0$ 인 경우 공간에 대한 차분을 1차 backward difference로 생각하자.\n",
"\n",
"$$\n",
"a \\frac{\\partial u}{\\partial x} \\approx a \\frac{u_{j}^n - u_{j-1}^n}{\\Delta x}\n",
"$$\n",
"\n",
"이를 정리하면 다음 기법을 만들 수 있다.\n",
"\n",
"$$\n",
"u_j^{n+1} = u_{j}^n - \\frac{a \\Delta t}{\\Delta x} (u_{j}^n - u_{j-1}^n).\n",
"$$\n",
"\n",
"#### Sine wave 예제\n",
"계산 영역은 $x \\in [-1, 1]$ 이고 초기 조건은 다음과 같다.\n",
"\n",
"$$\n",
"u(x,0) = \\sin(\\pi x)\n",
"$$\n",
"\n",
"양 끝점에서 경계 조건은 Periodic 조건을 주자. 수식적으로는\n",
"\n",
"$$\n",
"u(-1, t) = u(1, t).\n",
"$$\n",
"\n",
"시간 $t=1.5$ 일 때 해를 구하자.\n",
"\n",
"#### 계산 격자 구성, Solution array 구성\n",
"계산 영역을 $n_x + 1$개의 점으로 나누어보자.\n",
"\n",
"즉 격자점은 다음과 같다.\n",
"\n",
"$$\n",
"x_j = -1, -1 + \\Delta x, -1 + 2 \\Delta x, ..., 1 - \\Delta x, 1 ~~(1 \\le j \\le n_x +1)\n",
"$$\n",
"\n",
":::{figure-md} Grid\n",
"
\n",
"\n",
"Grid\n",
":::\n",
"\n",
"첫번째 격자점을 계산하기 위해서는 $x_0 = -1 - \\Delta x$ 값이 필요하다. \n",
"또한 마지막 격자점을 계산하기 위해서는 $x_{n_x+2} = 1 + \\Delta x$ 값이 필요하다.\n",
"\n",
"이를 대칭조건으로 구현하면 다음과 같다.\n",
"\n",
"$$\n",
"u_0^n = u_{n_x}^n \\\\\n",
"u_{n_x+2}^n = u_2^n\n",
"$$\n",
"\n",
"경계 조건을 위해서 Solution array는 격자점 + 2개의 경계 조건을 고려해서 $n_x+3$ 으로 구성한다.\n",
"\n",
"시간 간격은 $\\Delta t = 0.01$ 에 대해서 $n_x=50$ 인 경우 계산하면 다음과 같다."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "super-illustration",
"metadata": {},
"outputs": [],
"source": [
"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": "32416971",
"metadata": {},
"outputs": [],
"source": [
"def central(nx, u, dt, dx, a, du):\n",
" \"\"\"\n",
" Central difference\n",
"\n",
" Parameters\n",
" ----------\n",
" nx : integer\n",
" 등분 개수\n",
" u : array\n",
" Solution\n",
" dt : float\n",
" 시간간격\n",
" dx : float\n",
" 격자 간격\n",
" a : float\n",
" Wave speed\n",
" du : array\n",
" 증가량\n",
" \"\"\"\n",
" for i in range(1, nx+2):\n",
" du[i] = -0.5*a*(u[i+1] - u[i-1])/dx*dt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "hybrid-winner",
"metadata": {},
"outputs": [],
"source": [
"def central_v1(u, dt, dx, a):\n",
" \"\"\"\n",
" Central difference (vector version)\n",
"\n",
" Parameters\n",
" ----------\n",
" u : array\n",
" Solution\n",
" dt : float\n",
" 시간간격\n",
" dx : float\n",
" 격자 간격\n",
" a : float\n",
" Wave speed\n",
"\n",
" Return\n",
" ------\n",
" du : array\n",
" 증가량\n",
" \"\"\"\n",
" # Size of u : nx + 3\n",
" # 0, nx+2 (or -1) - ghost cell, \n",
" # 1 - nx+1 (or -2) - Inner\n",
" return -0.5*a*(u[2:] - u[:-2])/dx*dt"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "positive-yellow",
"metadata": {},
"outputs": [],
"source": [
"def bc_periodic(u):\n",
" \"\"\"\n",
" Boundary condition (peridoic)\n",
"\n",
" Parameter\n",
" ---------\n",
" u : array\n",
" solution\n",
" \"\"\"\n",
" # index (nx : -3), (nx+2 : -1)\n",
" u[0] = u[-3]\n",
" u[-1] = u[2]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "secondary-monaco",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Constants\n",
"a = 1.0\n",
"\n",
"nx = 50\n",
"dt = 0.01\n",
"t_target = 1.5\n",
"\n",
"# Make grid\n",
"x = np.linspace(-1, 1, nx+1)\n",
"dx = np.diff(x)[0]\n",
"\n",
"# Solution array\n",
"u = np.empty(nx+3)\n",
"du = np.zeros_like(u)\n",
"\n",
"# Initialize\n",
"u[1:-1] = np.sin(np.pi*x)\n",
"bc_periodic(u)\n",
"\n",
"# Calculation\n",
"t = 0\n",
"while abs(t - t_target) > 1e-8:\n",
" # Adjust time step to reach target time\n",
" dt = min(dt, t_target - t)\n",
" \n",
" # Periodic BC\n",
" bc_periodic(u)\n",
" \n",
" # Scheme\n",
" #du[1:-1] = central_v1(u, dt, dx, a)\n",
" central(nx, u, dt, dx, a, du)\n",
" \n",
" # Update\n",
" u += du\n",
" t += dt\n",
" \n",
"# Compare with exact solution\n",
"u_exact = np.sin(np.pi*(x-a*t))\n",
"plt.plot(x, u_exact)\n",
"plt.plot(x, u[1:-1])\n",
"plt.legend(['Exact', 'Computed'])"
]
},
{
"cell_type": "markdown",
"id": "cd80b9ec",
"metadata": {},
"source": [
"## 실습\n",
"- Central 기법에 대해 격자 개수와 시간 간격을 아래와 같이 달리하면셔 결과를 비교하시오.\n",
" * $N$ = 50, 100, 200\n",
" * $\\Delta t = 0.005, 0.01, 0.02, 0.05, 0.1$\n",
"\n",
"\n",
"- Upwind difference를 구현한 후, Sine Wave 문제를 해석하시오. Central 기법과 결과 차이를 비교하시오.\n",
"\n",
"\n",
"- 다음 Square Wave에 대해 Central difference 와 Upwind difference를 해석하시오.\n",
"\n",
"$$\n",
"u(x,0) = \\begin{cases}\n",
" 0, & \\text{if } x < -0.25 \\\\\n",
" 1, & \\text{if } -0.25 \\leq x < 0.25 \\\\\n",
" 0, & \\text{if } x > 0.25\n",
" \\end{cases}\n",
"$$\n",
"\n",
"- (Optional) $a < 0$ 일때 Upwind difference 기법은 공간에 대해 Forward 차분식을 적용해야 한다. $a=-1$인 경우에 대해 Upwind 기법을 구현하시오."
]
}
],
"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": "3.11.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}