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"\n",
"\n",
"\n",
"# Partial Differential Equations - Two Examples\n",
"\n",
"### Modules - Partial Differential Equations\n",
"\n",
"By Henning G. Hugdal, Håkon W. Ånes and Jon Andreas Støvneng \n",
"\n",
"Last edited: February 7th 2018 \n",
"___"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"In this module we will look at partial differential equations (PDEs), i.e. differential equations which have derivatives with respect to more than one variable. In physics one stumbles upon many differential equations, two examples being\n",
"\n",
"- the 2-dimensional Laplace equation\n",
" $$ \\left(\\frac{\\partial^2}{\\partial x^2} + \\frac{\\partial^2}{\\partial y^2}\\right)u = 0,$$\n",
" \n",
"- and the 1-dimensional heat equation\n",
" $$ \\frac{\\partial u}{\\partial t} = \\alpha \\frac{\\partial^2u}{\\partial x^2}.$$\n",
"\n",
"As an introduction to the discretization of partial differential equations, we will in this module give a couple of examples on how to discretize the above equations. This is known as finite-difference methods. There exists many discretization schemes, each having their own strenghts and weaknesses.\n",
"\n",
"First of all, it should be said that much of the difficulty of discretizing partial differential equation comes from the fact that the physics of the problem comes much more into play. For instance when discretizing equations describing fluid transport, the discretization has to be done in a way that uses the relevant information regarding the direction of flow etc."
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"## Laplace Equation\n",
"The Laplace equation can be discretized simply by using the second order central differences scheme. First we discretize the $x$- and $y$-axis using $x_i = x_{min} + i\\Delta x$, $i\\in[0,N_x]$, and $y_j = y_{min} + j\\Delta y$, $j\\in[0,N_y]$, where $\\Delta x = (x_{max}-x_{min})/N_x$ and $\\Delta y = (y_{max}-y_{min})/N_y$. Using this, we discretize $u$ by $u(x_i, y_j) = u_{i,j}$. This gives for the second derivative with respect to $x$\n",
"$$\\frac{\\partial^2 u}{\\partial x^2} \\rightarrow \\frac{u_{i+1,j} - 2u_{i,j} + u_{i-1,j}}{\\Delta x^2},$$\n",
"and similarly for the second derivative with respect to $y$,\n",
"$$\\frac{\\partial^2 u}{\\partial y^2} \\rightarrow \\frac{u_{i,j+1} - 2u_{i,j} + u_{i,j-1}}{\\Delta y^2}.$$ This gives the discretized Laplace equation\n",
"$$\\frac{u_{i+1,j} - 2u_{i,j} + u_{i-1,j}}{\\Delta x^2} +\n",
"\\frac{u_{i,j+1} - 2u_{i,j} + u_{i,j-1}}{\\Delta y^2} = 0.$$\n",
"\n",
"### Simple example\n",
"We can try to solve the above equation on the domain $x\\in[0,1]$, $y\\in[0,1]$, with the following boundary conditions (BCs):\n",
"\n",
"- $u(x,0) = u_a = 5$\n",
"\n",
"- $u(x,1) = u_b(x) = 5(1-\\sin(\\pi x))$\n",
"\n",
"- $u(0,y) = u_c = 5$\n",
"\n",
"- $\\frac{\\partial u(x,y)}{\\partial x}\\Big|_{x=1} = 0$.\n",
"\n",
"The first three of these boundary conditions are Dirichlet BCs which have been used in previous modules. The last is a Neumann BC, which requires special care since it doesn't give information about the value at the boundary directly.\n",
""
]
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"source": [
"The above image shows how we can choose to discretize the domain: We do not want to include the points we already know the values of, i.e. the points on the $x$- and $y$-axis, and the points on the line $y=1$. However, we have to include the points on the line $x=1$, since here the value of $u$ is unknown. This means that we have the following discretization of the $x$- and $y$-axis:\n",
"\n",
"- $x_i = (1+i)\\Delta x$, with $\\Delta x = \\frac{1}{N_x+1}$ and $i\\in [0, N_x]$.\n",
"\n",
"- $y_j = (1+j)\\Delta y$, with $\\Delta y = \\frac{1}{N_y+2}$ and $j \\in [0, N_y]$.\n",
"\n",
"Let us now treat the various boundary cases:\n",
"\n",
"- For $i=0$ we get\n",
" $$\\frac{u_{0,j+1} -2u_{0,j} + u_{0,j-1}}{\\Delta y^2} + \\frac{u_{1,j} -2u_{0,j} + u_c}{\\Delta x^2} = 0,$$\n",
" where $u_{-1,j}$ has been replaced by the value at the left boundary, $u_c$.\n",
" \n",
"- For $j=0$ we get\n",
" $$\\frac{u_{i,1} -2u_{i,0} + u_a}{\\Delta y^2} + \\frac{u_{i+1,0} -2u_{i,0} + u_{i-1,0}}{\\Delta x^2} = 0,$$\n",
" where $u_{i,-1}$ has been replaced by the value at the bottom boundary, $u_a$.\n",
"- For $j=N_y$ we get\n",
" $$\\frac{u_b(x_i) -2u_{i,N_y} + u_{i,N_y-1}}{\\Delta y^2} + \\frac{u_{i+1,N_y} -2u_{i,N_y} + u_{i-1,N_y}}{\\Delta x^2} = 0,$$\n",
" where $u_{i,N_y+1}$ has been replaced by the function giving the values at the top boundary, $u_b(x_i)$.\n",
"- For $i=N_x$ we get\n",
" $$\\frac{u_{N_x,j+1} -2u_{N_x,j} + u_{N_x,j-1}}{\\Delta y^2} + \\frac{u_{N_x+1,j} -2u_{N_x,j} + u_{N_x-1,j}}{\\Delta x^2} = 0.$$\n",
" Here we run into a problem: we don't have a value for $u_{N_x+1,j}$, which is a point outside the domain! However, we can find one using the boundary condition: we discretize the boundary condition,\n",
" $$ \\frac{\\partial u(x,y)}{\\partial x} \\rightarrow \\frac{u_{i+1,j} - u_{i-1,j}}{2\\Delta x},$$\n",
" which gives at the boundary\n",
" $$\\frac{u_{N+1,j} - u_{N-1,j}}{2\\Delta x} = 0.$$\n",
" Hence we get that $u_{N+1,j} = u_{N-1,j}$, and get the following equation at the right boundary:\n",
" $$\\frac{u_{N_x,j+1} -2u_{N_x,j} + u_{N_x,j-1}}{\\Delta y^2} + \\frac{-2u_{N_x,j} + 2u_{N_x-1,j}}{\\Delta x^2} = 0.$$\n",
" Notice that we get a factor $2$ in front of $u_{N_x-1,j}$."
]
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"source": [
"In the above, all constants will be moved to the right hand side, and hence make up the vector ${\\bf{b}}$ in the matrix equation\n",
"$$A{\\bf{u}} = {\\bf{b}}.$$\n",
"It is also important to note, that in the corners of the domain, i.e. at the points $(i,j) = (0,0)$, $(N_y,0)$, $(0,N_x)$ and $(N_y,N_x)$ we must combine two of the above boundary conditions.\n",
"\n",
"We can now start constructing the matrix equation using the above results. For simplicity we will set $\\Delta x = \\Delta y$, which allows us to multiply them out. We then get\n",
"$$\\left(\\matrix{\n",
"-4 & 1 & 0 &0 &...& 0 & 1 & 0 &0&...\\\\\n",
"1 & -4 & 1 &0&...& 0 & 0 & 1 &0&...\\\\\n",
"0& 1 & -4& 1& ...& 0 &0&0&1&...\\\\\n",
"\\vdots& \\vdots& \\vdots& \\vdots& \\vdots& \\vdots &\\vdots&\\vdots&\\vdots&\\ddots&\n",
"}\\right)\n",
"\\left(\\matrix{\n",
"u_{0,0}\\\\\n",
"u_{1,0}\\\\\n",
"u_{2,0}\\\\\n",
"\\vdots\\\\\n",
"u_{N_x,0}\\\\\n",
"u_{0,1}\\\\\n",
"u_{1,1}\\\\\n",
"u_{1,2}\\\\\n",
"\\vdots\n",
"}\\right) = \\left(\\matrix{\n",
"-u_c-u_a\\\\\n",
"-u_a\\\\\n",
"-u_a\\\\ \\vdots}\\right)$$\n",
"Here A is a pentadiagonal, $N\\times N$-matrix, with $N=N_x\\cdot N_y$, and ${\\bf b}$ is a vector with length $N$."
]
},
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"cell_type": "markdown",
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"source": [
"We now start solving the above system. First we need to import the necessary packages, and then constuct the matrix $A$ and vector ${\\bf b}$. It can be difficult to get all the elements right, and a good tip is to discretize the system using just a few grid points, and then check the implementation using this small grid."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy.linalg as linalg\n",
"import numpy as np\n",
"\n",
"# Set common figure parameters:\n",
"newparams = {'figure.figsize': (16, 6), 'font.size': 20}\n",
"plt.rcParams.update(newparams)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Set the number of grid points\n",
"Nx = 50\n",
"dx = 1/(Nx+1)\n",
"x = np.linspace(dx, 1, Nx+1)\n",
"\n",
"dy = dx\n",
"Ny = int(1/dy - 2)\n",
"N = (Nx+1)*(Ny+1)\n",
"y = np.linspace(dy, 1-dx, Ny+1)\n",
"\n",
"# Set constants at boundary\n",
"ua = 5\n",
"ub = 5*(1-np.sin(np.pi*x))\n",
"uc = 5\n",
"\n",
"### Construct the matrix A\n",
"A = np.zeros([N,N])\n",
"\n",
"for i in range(N):\n",
" # Set the diagonals to -4\n",
" A[i, i] = -4\n",
" # Set the non-zero off-diagonals to 1\n",
" if i > 0:\n",
" A[i, i-1] = 1\n",
" if i < N-1:\n",
" A[i, i+1] = 1\n",
" if i < N-Nx-1:\n",
" A[i+Nx+1, i] = 1\n",
" A[i, i+Nx+1] = 1\n",
" \n",
"for i in range(N):\n",
" # Some elements must be changed to 2 due to the Neumann BCs\n",
" if (i+1)%(Nx+1) == 0:\n",
" A[i,i-1] = 2\n",
" \n",
" # In addition some elements must be set to zero, since\n",
" # the elements are taken care of by terms in b\n",
" if i > 0 and i < N - 1 and (i+1)%(Nx+1) == 0:\n",
" A[i, i+1] = 0\n",
" A[i+1, i] = 0\n",
"\n",
"### Construct the right hand side vector b:\n",
"b = np.zeros(N)\n",
"\n",
"# For j = 0, set elements to -ua\n",
"b[0:Nx+1] = - ua\n",
"\n",
"# For i = 0, set the elements to -uc\n",
"indices = np.mod(range(N),Nx+1) == 0\n",
"b[indices] += -uc\n",
"\n",
"# For j = Ny, set elements to -ub(x_i)\n",
"for i in range(Nx+1):\n",
" b[N-Nx-1+i] += -ub[i]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we solve the matrix equation using ``linalg.solve()``, and plot the result."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Solve the system using linalg\n",
"u = linalg.solve(A,b)\n",
"\n",
"# Reshape solution array to be able to plot it\n",
"u_ = u.reshape(Ny+1,Nx+1)\n",
"plt.figure(figsize=(16, 8))\n",
"plt.contourf(x, y, u_, 100)\n",
"plt.colorbar()\n",
"plt.ylabel('y')\n",
"plt.xlabel('x')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Heat equation\n",
"The 1D heat equation is a little bit more tricky to discretize. For the spatial discretization, we again use the second order central differences scheme, resulting in the semi-discretized equation\n",
"$$\\frac{d}{d t}u(x_i,t) = \\alpha \\frac{u(x_{i+1},t) - 2u(x_i,t) + u(x_{i+1},t)}{\\Delta x^2}.$$\n",
"The problem is how to discretize the time-derivative. One guess might be to use the simple explicit Euler method, but this turns out to be unconditionally unstable! Therefore, we try the implicit, or forward, Euler method. This results in the equation\n",
"$$ \\frac{u_i^{n+1} - u_i^n}{\\Delta t} = \\alpha \\frac{u_{i+1}^{n+1} - 2u_i^{n+1} + u_{i+1}^{n+1}}{\\Delta x^2},$$\n",
"where we have discretized the time $t$ by $t_n = t_{start} + n\\Delta t$, and the superscript in $u$ denotes the time step.\n",
"Since one uses forward Euler in time and central differences in space, this is often called the Forward-Time Centered-Space (FTCS) scheme."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can rearrange the above equation to express the unknown values in terms of the known quantities:\n",
"$$ u_i^{n+1}(1+2C) - C(u_{i+1}^{n+1} + u_{i-1}^{n+1}) = u_i^n,$$\n",
"where we have defined $C \\equiv \\alpha\\Delta t/\\Delta x^2$. This means that we again have to solve a linear system of equations.\n",
"From the above we see that, in addition to boundary conditions for $u$, we also need an initial condition for $u$ at time $t=t_{start}$ corresponding to $u_i^0$.\n",
"\n",
"It is important to note that the above method is numerically stable if and only if $|C|\\leq 0.5$. Hence we have to check that we choose the number of grid points and time stepts such that this condition is fulfilled."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Simple Example\n",
"\n",
"We will solve the 1D heat equation using the initial condition\n",
"$$u(t=0) = 5\\cos(\\pi x)$$\n",
"and the boundary conditions $u(x=0) = 2$ and $u(x=1) = 10$. We choose $\\alpha = 0.005$, and solve the heat equation from $t=0$ to $t=10$.\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"C = 0.5\n"
]
}
],
"source": [
"alpha = 0.005\n",
"Nx = 100\n",
"dx = 1/Nx\n",
"x = np.linspace(0, 1, Nx + 1)\n",
"\n",
"Nt = 1000\n",
"dt = 10/Nt\n",
"\n",
"# Boundary condition\n",
"ua = 2\n",
"ub = 10\n",
"\n",
"C = alpha*dt/dx**2\n",
"print(\"C = \", C)\n",
"\n",
"### Construct solution matrix\n",
"A = np.zeros([Nx + 1, Nx + 1])\n",
"\n",
"# Diagonals equal 1+2C\n",
"for i in range(Nx + 1):\n",
" A[i, i] = 1 + 2*C\n",
"\n",
"# Off-diagonals equal -C\n",
" if i > 0:\n",
" A[i, i - 1] = -C\n",
" if i < Nx:\n",
" A[i, i + 1] = -C\n",
"\n",
"# Construct boundary condition matrix b where only first and last term are non-zero:\n",
"b = np.zeros(Nx + 1)\n",
"b[0] = C*ua\n",
"b[-1] = C*ub"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now iterate over time, and solve the system of equations for each time-step. We plot the solution at regular time-intervals."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Intitial condition\n",
"u = np.zeros([Nt+1, Nx+1])\n",
"u[0,:] = 5*np.cos(np.pi*x)\n",
"\n",
"plt.figure()\n",
"plt.plot(x, u[0])\n",
"\n",
"for n in range(Nt):\n",
" u[n+1] = linalg.solve(A, b+u[n])\n",
" \n",
" if n%100 == 0:\n",
" plt.plot(x, u[n+1])\n",
"plt.xlabel('x')\n",
"plt.xlim([0, 1])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to visualize the time-evolution of the system better, we can make an animation. The following code defines functions which allows us to make and display animations.\n",
"\n",
"NB: The animation may not work in all browsers."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from matplotlib import animation\n",
"from IPython.display import HTML\n",
"\n",
"# Set new figure parameters\n",
"newparams = {'axes.labelsize': 11, 'axes.linewidth': 0.5, 'savefig.dpi': 300, \n",
" 'lines.linewidth': 1.0, 'figure.figsize': (3, 2),\n",
" 'ytick.labelsize': 5, 'xtick.labelsize': 5,}\n",
"plt.rcParams.update(newparams);\n",
"\n",
"# First set up the figure, the axis, and the plot element we want to animate\n",
"fig = plt.figure()\n",
"ax = plt.axes(xlim=(0, 1), ylim=(-6, 10))\n",
"line, = ax.plot([], [], lw=1)\n",
"\n",
"# Initialization function: plot the background of each frame\n",
"def init():\n",
" line.set_data([], [])\n",
" return line,\n",
"\n",
"# Animation function which updates figure data. This is called sequentially\n",
"def animate(i):\n",
" line.set_data(x, u[i,:])\n",
" return line,\n",
"\n",
"# Call the animator. blit=True means only re-draw the parts that have changed.\n",
"anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
" frames=Nt, interval=20, blit=True)\n",
"\n",
"plt.close(anim._fig)\n",
"\n",
"# Call our new function to display the animation\n",
"HTML(anim.to_html5_video())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the solution evolves towards the expected solution - a straight line starting in 2 at $x=0$ and ending in 10 at $x=1$."
]
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"### References\n",
"[1] R.H. Pletcher, J. C. Tannehill, D. Anderson. *Computational Fluid Mechanics and Heat Transfer*, CRC Press (2011)"
]
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