{ "cells": [ { "cell_type": "markdown", "id": "1d2eb3be-2943-4811-967e-c481ad04bc2b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Diffusive Equation\n", "\n", "The diffusive equation is described by\n", "\n", "$$\n", "\\partial_t \\phi - \\partial_{\\alpha}\\left( \\nu \\partial_{\\alpha}\\phi \\right) = 0\n", "$$(df-eq-lb)\n", "\n", "where $\\phi(\\alpha,t)$ is a time and space dependent parameter and $\\nu$ is diffusive coeficient. \n" ] }, { "cell_type": "markdown", "id": "c7b2cd44-0e05-4597-aee1-88ea4330f996", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Numerical Discretization" ] }, { "cell_type": "markdown", "id": "117e5e3f-fda3-4340-ae8c-87c35b804e20", "metadata": {}, "source": [ "```{figure} mesh-1-diffusive.svg\n", "---\n", "scale: 250%\n", "align: center\n", "name: mesh-1-diffusive\n", "---\n", "1D regular grid example for diffusive equation.\n", "```" ] }, { "cell_type": "markdown", "id": "37c8a5f4-2739-475b-b4b6-c514b4fecd85", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### FDM Discretization\n", "\n", "Discretizing the Eq. {eq}`df-eq-lb` through finite diference method, we have for forward time and central space (FTCS) discretizations:\n", "\n", "$$\n", "\\partial_t \\phi - \\partial_{\\alpha}\\left( \\nu \\partial_{\\alpha}\\phi \\right) = \\frac{\\phi(x,t + \\Delta_{t}) - \\phi(x,t) }{\\Delta_{t}} - \\nu\\frac{ \\phi(x - \\Delta_{x},t) -2\\phi(x,t) + \\phi(x + \\Delta_{x},t) }{\\Delta_{x}^{2}} =0,\n", "$$\n", "\n", "for $\\nu$ constant and isolating the term $u(x,t + \\Delta_{t})$, we can describe the $\\phi$ time evolution:\n", "\n", "$$\n", "\\phi(x,t + \\Delta_{t}) = \\phi(x,t) + \\frac{\\nu\\Delta_{t}}{\\Delta_{x}^{2}} \\left( \\phi(x - \\Delta_{x},t) -2\\phi(x,t) + \\phi(x + \\Delta_{x},t) \\right) .\n", "$$" ] }, { "cell_type": "markdown", "id": "320b11c7-d9a3-4634-bb62-1388136ac2be", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Lattice Boltzmann Equation\n", "\n", "Describing the problem through the BGK lattice Boltzmann equation (BGK-LB):\n", "\n", "$$\n", "f_i( x_{\\alpha} + c_{i,\\alpha} \\delta t, t+\\delta t) = f_i(x_{\\alpha}, t) -\\left( \\frac{ f_{i} - f_{i}^{eq} }{ \\tau } \\right), \n", "$$(LB-df-Eq)\n", "\n", "where the equilibrium distribution function is defined by\n", "\n", "$$\n", "f^{eq}_{i} = w_{i}\\phi(x_{\\alpha}, t),\n", "$$\n", "\n", "and the equilibrium moments are given by \n", "\n", "$$\n", "\\displaystyle\\sum_{i=0} f_{i}^{eq}=\\phi, \\quad \\quad \\displaystyle\\sum_{i}f_{i}^{eq} c_{i,\\alpha} =0 \\quad \\quad \\textrm{and} \\quad \\quad \\displaystyle\\sum_{i}f_{i}^{eq} c_{i,\\alpha} c_{i,\\beta} =c_{s}^{2} \\phi \\delta_{\\alpha\\beta}.\n", "$$(moments-fi-df)\n", "\n", "Through Chapman–Enskog analysis, it is demonstrated that the first-order non-equilibrium moment describes the pressure gradient and, consequently, the average velocity:\n", "\n", "$$\n", "m^{neq}_{\\alpha} = \\displaystyle\\sum_{i} c_{i,\\alpha}\\left( f_i-f_i^{eq}\\right) = -(c_{s}^{2} \\tau \\delta_{t})\\partial_{\\alpha}\\phi \\quad \\quad \\textrm{and} \\quad\\quad \\tau = \\displaystyle\\frac{\\nu}{c_{s}^{2} \\delta_{t}} +\\frac{1}{2}.\n", "$$" ] }, { "cell_type": "markdown", "id": "a1f0e00d-c032-414a-8aff-b666ba180f7d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "#### Lattice Direction Moments" ] }, { "cell_type": "code", "execution_count": 2, "id": "c8dd6283-a6ef-4060-8675-30eb45b800cf", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "from pylab import *\n", "from __future__ import division\n", "from sympy import *\n", "import numpy as np\n", "from sympy import S, collect, expand, factor, Wild\n", "from sympy import fraction, Rational, Symbol\n", "from sympy import symbols, sqrt, Rational\n", "import sympy as sp\n", "from IPython.display import display, Math, Latex\n", "#-------------------------------------------------Símbolos----------------------------------------------\n", "omega, p, w = symbols('omega, \\\\phi, w')\n", "wi, cx, cy, cs = symbols('w_{i} c_{x} c_{y} c_{s}')\n", "fi, f0, f1, f2, f3, f4, f5, f6, f7, f8, = symbols('f_{i} f_{0} f_{1} f_{2} f_{3} f_{4} f_{5} f_{6} f_{7} f_{8}')\n", "#-------------------------------------------------Funções----------------------------------------------\n", "feq = Function('feq')(wi, cx, cy)\n", "fneq = Function('fneq')(wi, cx, cy)\n", "f = Function('f')(fi)\n", "#----------------------------------------------Lattice-D2Q9---Variáveis----------------------------------------------\n", "fi=np.array([f1,f2,f3,f4,f5,f6,f7,f8])\n", "w0=Rational(4,9);w1=Rational(1,9);w2=Rational(1,36)\n", "wi=np.array([w0,w1,w1,w1,w1,w2,w2,w2,w2])\n", "cx=np.array([0,1,0,-1,0,1,-1,-1,1])\n", "cy=np.array([0,0,1,0,-1,1,1,-1,-1])\n", "as2=Rational(3)\n", "cs2=1/as2\n", "#-------------------------------------------------Calc.Func------------------------------------------------\n", "f= fi\n", "feq=wi*p" ] }, { "cell_type": "code", "execution_count": 3, "id": "2147848c-6015-4c81-8eee-6f09e6191c81", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\underbrace{\\sum_{i=0} f_{i}^{eq} =\\sum_{i=0} f_{i} }_{\\textrm{Zero-Order Moment}} =\\phi,\\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,x} }_{\\textrm{x-First-Order Moment}} =0,\\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,y} }_{\\textrm{y-First-Order Moment}} =0,\\\\ \\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,x}c_{i,x} }_{\\textrm{xx-Second-Order Moment}} =\\frac{\\phi}{3},\\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,x}c_{i,y} }_{\\textrm{xy-Second-Order Moment}} =0 \\quad \\quad and \\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,y}c_{i,y} }_{\\textrm{yy-Second-Order Moment}} =\\frac{\\phi}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a0=simplify(sum(feq))\n", "ax=simplify(sum(feq*cx))\n", "ay=simplify(sum(feq*cy))\n", "axx=simplify(sum(feq*cx*cx))\n", "axy=simplify(sum(feq*cx*cy))\n", "ayy=simplify(sum(feq*cy*cy))\n", "display(Math(r\"\\underbrace{\\sum_{i=0} f_{i}^{eq} =\\sum_{i=0} f_{i} }_{\\textrm{Zero-Order Moment}} =\" + sp.latex(a0) \n", " +r\",\\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,x} }_{\\textrm{x-First-Order Moment}} =\" + sp.latex(ax)\n", " +r\",\\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,y} }_{\\textrm{y-First-Order Moment}} =\" + sp.latex(ay)\n", " +r\",\\\\ \\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,x}c_{i,x} }_{\\textrm{xx-Second-Order Moment}} =\" + sp.latex(axx)\n", " +r\",\\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,x}c_{i,y} }_{\\textrm{xy-Second-Order Moment}} =\" + sp.latex(axy)\n", " +r\" \\quad \\quad and \\quad \\quad \\underbrace{\\sum_{i=0} f_{i}^{eq}c_{i,y}c_{i,y} }_{\\textrm{yy-Second-Order Moment}} =\" + sp.latex(ayy)))" ] }, { "cell_type": "markdown", "id": "16f5cc23-a6a1-4fe4-a8b6-1488556126a7", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "#### Chapmann-Enskog Analysis\n", "\n", "```{toggle}\n", "Applying the Chapmann-Enskog procedure to LB equation, we expand the term $f_{i}\\left(\\boldsymbol{x}+\\boldsymbol{e}_i \\Delta t, t+\\Delta t\\right)$ in a Taylor series to recover the derivative form of the equation, i.e.,\n", "\n", "$$\n", "f_{i}\\left( x_{\\alpha} + c_{i,\\alpha} \\Delta t, t+\\Delta t\\right)- f_{i}( x_{\\alpha}, t)=\\displaystyle\\sum_{j=1}^{\\infty}\\frac{\\Delta t^{j}}{j!}D_{t}^{j}f_{i}= -\\left( \\frac{ f_{i} - f_{i}^{eq} }{ \\tau } \\right).\n", "$$(EqExp-df-Eq)\n", "\n", "Rescaling the dimensionless form of the Eq. {eq}`EqExp-df-Eq` in terms of the Knudsen number ($Kn$), we have\n", "\n", "$$\n", "\\displaystyle \\sum^{\\infty}_{j=1} \\frac{Kn^{(j-1)}}{j!} D_{t}^{j} f_{i} = - \\frac{1}{Kn}\\left( \\frac{ f_{i} - f_{eq,i} }{ \\tau } \\right) \\quad \\quad \\rightarrow \\quad \\quad \\displaystyle \\sum^{\\infty}_{j=1} \\frac{Kn^{(j)}}{j!} D_{t}^{j} f_{i} = - \\frac{ f_{i} - f_{i}^{eq} }{ \\tau },\n", "$$\n", "\n", "applying the asymptotic expansion in both the distribution function ($f_{i}=f_{i}^{(0)}+Kn f_{i}^{(1)} + Kn^{2} f_{i}^{(2)}+\\cdots$) and time partial derivative ($\\partial_{t}=\\partial_{t}^{(0)}+ Kn \\partial_{t}^{(1)}+Kn^{2} \\partial_{t}^{(2)}+\\cdots$), and separating the equation in orders up to the order $Kn^{2}$:\n", "\n", "$$\n", "\\begin{array}{ll}\n", " (Kn^{(0)}):& f_{i}^{(0)}= f_{i}^{eq},\\\\\n", " (Kn^{(1)}):& \\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)f_{i}^{(0)}= - \\displaystyle\\frac{ f_{i}^{(1)} }{ \\tau } , \\\\\n", " (Kn^{(2)}):& \\partial_{t}^{(1)} f_{i}^{(0)} + \\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)f_{i}^{(1)} + \\displaystyle\\frac{\\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)^{2} f_{i}^{(0)}}{2}= - \\displaystyle\\frac{ f_{i}^{(2)} }{ \\tau },\\\\\n", " \\textrm{ou}\\\\\n", " (Kn^{(2)}):& \\partial_{t}^{(1)} f_{i}^{(0)} + \\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)\\displaystyle\\left(1 - \\frac{1}{2\\tau}\\right) f_{i}^{(1)} = - \\displaystyle\\frac{ f_{i}^{(2)} }{ \\tau } \\quad\\quad \\rightarrow \\quad\\quad f_{i}^{(1)}\\textrm{ Formulation} \\\\\n", " \\textrm{ou}\\\\\n", " (Kn^{(2)}):& \\partial_{t}^{(1)} f_{i}^{(0)} + \\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)^{2} \\displaystyle\\left(\\frac{1}{2} - \\tau\\right) f_{i}^{(0)} = - \\displaystyle\\frac{ f_{i}^{(2)} }{ \\tau } \\quad\\quad \\rightarrow \\quad\\quad f_{i}^{(0)}\\textrm{ Formulation}.\n", " \\end{array}\n", "$$(Chap-Kn-df-Eq)\n", "\n", "##### Zero-Order Moment Balance\n", "\n", "To retrieve the balance equation, we sum the Eq. {eq}`Chap-Kn-df-Eq` for $Kn^{(1)}$ and $Kn^{(2)}$ over $\\sum_{i=0} $:\n", "\n", "$$\n", "\\begin{array}{l}\n", "(Kn^{(1)}): \\displaystyle\\sum_{i}\\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)f_{i}^{(0)}= \\displaystyle\\sum_{i} \\left(- \\displaystyle\\frac{ f_{i}^{(1)} }{ \\tau } \\right),\\\\\n", "(Kn^{(1)}): \\partial_{t}^{(0)} \\phi =0,\n", "\\end{array}\n", "$$\n", "\n", "and\n", "\n", "$$\n", "\\begin{array}{l}\n", "(Kn^{(2)}): \\displaystyle\\sum_{i}\\left( \\partial_{t}^{(1)} f_{i}^{(0)} + \\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right)^{2} \\displaystyle\\left( \\frac{1}{2}-\\tau\\right) f_{i}^{(0)} \\right) = \\displaystyle\\sum_{i}\\left( - \\displaystyle\\frac{ f_{i}^{(2)} }{ \\tau } \\right), \\\\\n", "(Kn^{(2)}): \\partial_{t}^{(1)}\\phi + \\left( \\displaystyle\\frac{1}{2}-\\tau\\right) \\partial_{\\alpha}\\partial_{\\beta} \\left(c_{s}^{2} \\phi \\delta_{\\alpha\\beta} \\right) =0. \n", "\\end{array}\n", "$$\n", "\n", "or\n", "\n", "$$\n", "\\begin{array}{l}\n", "(Kn^{(2)}):& \\displaystyle\\sum_{i}\\left[ \\partial_{t}^{(1)} f_{i}^{(0)} + \\left(1-\\displaystyle\\frac{1}{2\\tau}\\right)\\left( \\partial_{t}^{(0)} + c_{i,\\alpha}\\partial_{\\alpha} \\right) f_{i}^{(1)} \\right]= \\displaystyle\\sum_{i}\\left( - \\displaystyle\\frac{f_{i}^{(2)}}{\\tau} \\right), \\nonumber \\\\\n", "(Kn^{(2)}):& \\partial_{t}^{(1)}\\phi + \\left(1-\\displaystyle\\frac{1}{2\\tau}\\right) m^{(1)}_{\\alpha} = 0.\n", "\\end{array}\n", "$$(df-Kn1-0-B0)\n", "\n", "where $m^{(1)}_{\\alpha}$ is the first-order moment of $f_{i}^{(1)}$ and $\\sum_{i=1}f_{i}^{(j)}=0$ for $j\\geq 1$ due to imposition of $\\phi$ conservation. To compute the moment $m^{(1)}_{\\alpha}$, we multiply Eq. {eq}`Chap-Kn-df-Eq` by $c_{i,\\alpha}$ and sum over all lattice directions:\n", "\n", "$$\n", "\\begin{array}{l}\n", "(Kn^{(1)}): \\displaystyle\\sum_{i}c_{i,\\alpha}\\left( \\partial_{t}^{(0)} + e_{\\beta,i}\\partial_{\\beta} \\right)f_{i}^{(0)}= \\displaystyle\\sum_{i} c_{i,\\alpha} \\left( -\\frac{f_{i}^{(1)}}{\\tau} \\right),\\\\\n", "(Kn^{(1)}): m^{(1)}_{\\alpha} =-\\tau \\partial_{\\beta}\\left( c_{s}^{2} \\phi \\delta_{\\alpha\\beta} \\right).\n", "\\end{array}\n", "$$(df-Kn0-B1)\n", "\n", "\n", "By substituting Eq. {eq}`df-Kn0-B1` into Eq. {eq}`df-Kn1-0-B0`, we recover the Eq. {eq}`df-eq-lb`, where $\\nu=c_{s}^{2}(\\tau-1/2)$. In the regularized formulation of the lattice Boltzmann equation, the first-order correction is approximated as $f_{i}^{(1)}\\approx (f_{i}-f_{i}^{(0)})=f_{i}^{neq}$, where higher-order Knudsen moments are filtered out and the collision term is reformulated in terms of $f_{i}^{neq}$.\n", "```" ] }, { "cell_type": "markdown", "id": "12d0efed-4938-41ee-90d6-e6971f1f1146", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "#### Boundary Conditions\n", "\n", "The boundary conditions for the lattices can be derived by solving a linear system of known moments." ] }, { "cell_type": "markdown", "id": "ed35c46d-0d61-4be2-9c27-68f579754ab9", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "| D1Q2: | Boundaries | | Layers | | |\n", "|------|-----------------|---|---------------------------------------------------------------------------------|---|---------------------------------------------------------------------------------|\n", "| | | | West | | East |\n", "| | Unknown $f_{i}$ | | $f_2=\\phi_{e} - f_1$ | | $f_1=\\phi_{w} - f_2$ |\n", "| | | | | | |\n", "| D1Q3: | Boundaries | | Layers | | |\n", "| | | | West | | East |\n", "| | Unknown $f_{i}$ | | $f_2=\\phi_{e} - f_1 - f_0$ | | $f_1=\\phi_{w} - f_2 - f_0$ |\n", "| | | | | | |\n", "" ] }, { "cell_type": "markdown", "id": "58ae6184-eb7d-4b14-a130-9ea979df3013", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## 1st Benchmark: Single sine mode on a finite rod (Dirichlet)\n", "\n", "PDE: $(\\phi_t = \\partial_{x}(\\nu\\partial_{x}\\phi), (00)$\n", "\n", "BC: $(\\phi(0,t)=\\phi(L,t)=0)$\n", "\n", "IC: $\\phi(x,0)=\\sin \\left(\\frac{\\pi x}{L}\\right)$\n", "\n", "**Solution**\n", "\n", "$$\n", "\\phi(x,t)=\\sin\\left(\\frac{\\pi x}{L}\\right) \\exp \\left(-\\nu \\frac{\\pi^2}{L^2} t\\right).\n", "$$" ] }, { "cell_type": "markdown", "id": "30600828-bef4-43b4-b3ef-ed507f7d4adc", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### LBM D1Q3 Solution ($\\tau=1$)" ] }, { "cell_type": "code", "execution_count": 48, "id": "66053dc8-8fd5-4ef3-b244-3b372c52c293", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dx=5.0000e-02\t dt=1.2500e-02\t nt=160\n", "nue=0.1667\t tau=1.0000\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "#--------------------------------------- Parameters (physical units) ------------------------------------------\n", "L = 1.0 # Length of the domain\n", "nu = 0.1/3.0 # Diffusion coefficient\n", "t_end = 2.0 # Total simulation time\n", "#--------------------------------------- Lattice-Properties-D1Q3 ----------------------------------------------\n", "cs=1.0/np.sqrt(3.0);\n", "w = np.array([4.0/6.0, 1.0/6.0, 1.0/6.0],dtype=\"float64\")\n", "cx = np.array([0, 1, -1],dtype=\"int8\") \n", "#------------------------------------- Parameters (numerical units) -------------------------------------------\n", "Nx=21 # Domain Length\n", "dx = L / (Nx-1) # Spatial step size\n", "c=1.0*2**(2) # c=dx/dt\n", "dt=dx/c # Time step value\n", "nt = int(t_end / dt) # Time step number\n", "nue=nu/(c*dx) # Diffusion coefficient\n", "tau=nue/cs**2+0.5 # Relaxation Time\n", "print(f\"dx={dx:.4e}\\t dt={dt:.4e}\\t nt={nt:d}\") # Print values for check\n", "print(f\"nue={nue:.4f}\\t tau={tau:.4f}\")\n", "#--------------------------------- Initialization - Numerical Arrays -----------------------------------------\n", "T = np.zeros((Nx),dtype=\"float64\")\n", "x = np.linspace(0, Nx-1, Nx)\n", "T = np.sin(np.pi * x / (Nx-1))\n", "f = np.zeros((3,Nx),dtype=\"float64\")\n", "fp = np.zeros((3,Nx),dtype=\"float64\")\n", "for k in range(0,3):\n", " fp[k,:]=w[k]*T[:]\n", "#--------------------------------- Initialization - Save Data Arrays -----------------------------------------\n", "snaps=5 # number of states saved over time including 0 and t_end\n", "T_snaps = np.empty(snaps, dtype=object) # array field used to same data over time\n", "snaps_id = np.linspace(0, nt, snaps, dtype=\"int16\") # timesteps to take the field\n", "snap_index = {sid: i for i, sid in enumerate(snaps_id)}\n", "for i in range(snaps):\n", " T_snaps[i] = np.zeros((Nx), dtype=\"float64\")\n", "T_snaps[0][:]=T[:]\n", "#----------------------------------------- Maind Loop --------------------------------------------------------\n", "for t in range(nt):\n", " #-----------------streaming-------------------\n", " for k in range(0,3):\n", " f[k,:]=np.roll(fp[k,:], cx[k], axis=0)\n", " #-----------------Boundaries-----------------------\n", " f[1,0]= 0.0 - f[0,0]-f[2,0]\n", " f[2,Nx-1]= 0.0 - f[0,Nx-1]-f[1,Nx-1]\n", " #----------------------Macro------------------\n", " T[:]=f[0,:]+f[1,:]+f[2,:]\n", " #---------------------save-snaps--------------\n", " if t+1 in snaps_id:\n", " i = snap_index[t+1]\n", " T_snaps[i][:]=T[:]\n", " #--------------------Collision----------------\n", " for k in range(0,3):\n", " fp[k,:]=f[k,:] - (f[k,:] - w[k]*T[:])/tau" ] }, { "cell_type": "markdown", "id": "d0c1d9a6-e277-4c47-a7e0-a1f145a74237", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### FDM Solution" ] }, { "cell_type": "code", "execution_count": 52, "id": "592d1318-4a54-4a76-b437-a337860a6c04", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input", "hide-output" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dx=5.0000e-02\t dt=1.2500e-02\t nt=160\n", "nue=0.1667\t tau=1.0000\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "#--------------------------------------- Parameters (physical units) ------------------------------------------\n", "L = 1.0 # Length of the domain\n", "nu = 0.1/3.0 # Diffusion coefficient\n", "t_end = 2.0 # Total simulation time\n", "#------------------------------------- Parameters (numerical units) -------------------------------------------\n", "Nx=21 #Square Domain Length\n", "dx = L / (Nx-1) # Spatial step size\n", "c=1.0*2**(2) # c=dx/dt\n", "dt=dx/c # Time step size\n", "nt = int(t_end / dt) # Time step number\n", "print(f\"dx={dx:.4e}\\t dt={dt:.4e}\\t nt={nt:d}\") # Print values for check\n", "print(f\"nue={nue:.4f}\\t tau={tau:.4f}\")\n", "#--------------------------------- Initialization - Numerical Arrays -----------------------------------------\n", "Tf = np.zeros((Nx),dtype=\"float64\")\n", "x = np.linspace(0, Nx-1, Nx)\n", "Tf = np.sin(np.pi * x / (Nx-1))\n", "Tfp = np.zeros((Nx),dtype=\"float64\")\n", "#--------------------------------- Initialization - Save Data Arrays -----------------------------------------\n", "snaps=5 # number of states saved over time including 0 and t_end\n", "Tf_snaps = np.empty(snaps, dtype=object) # array field used to same data over time\n", "snaps_id = np.linspace(0, nt, snaps, dtype=\"int16\") # timesteps to take the field\n", "snap_index = {sid: i for i, sid in enumerate(snaps_id)}\n", "for i in range(snaps):\n", " Tf_snaps[i] = np.zeros((Nx), dtype=\"float64\")\n", "Tf_snaps[0][:]=Tf[:]\n", "#----------------------------------------- Maind Loop --------------------------------------------------------\n", "for t in range(nt):\n", " #--------------------Time iteration-----------\n", " Tfp[:]=Tf[:] + dt * nu * ( np.roll(Tf[:], 1, axis=0) -2.0*Tf[:] + np.roll(Tf[:], -1, axis=0) ) / dx**2\n", " Tf[:]=Tfp[:]\n", " Tf[0]= 0.0 \n", " Tf[Nx-1]= 0.0\n", " #---------------------save-snaps--------------\n", " if (t+1) in snaps_id:\n", " i = snap_index[t+1]\n", " Tf_snaps[i][:]=Tf[:]" ] }, { "cell_type": "markdown", "id": "9ea91374-77b0-4d1a-9b42-1fc4c39c7f8d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Numerical and Analytical Comparisson" ] }, { "cell_type": "code", "execution_count": 53, "id": "23947517-ca22-414e-8c8c-af56fd626bab", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "#--------------------------------------- Parameters (physical units) ------------------------------------------\n", "L = 1.0 # Domain length\n", "nu = 0.1/3.0 # Diffusion coefficient\n", "t_end = 2.0 # Total simulation time\n", "snaps=5 # number of states saved over time including 0 and t_end\n", "#------------------------------------- Parameters (numerical units) -------------------------------------------\n", "Nx = 21 # Number of spatial points\n", "#--------------------------------------- Plot Results -------------------------------------------------------\n", "def T_exact(x, t, L, nu): # ---------------- exact solution ----------------\n", " return np.sin(np.pi * x / L) * np.exp(-nu * (np.pi / L)**2 * t)\n", "xl = np.linspace(0, L, Nx)\n", "times = np.linspace(0, t_end, snaps, dtype=\"float64\") # timesteps to take the field\n", "plt.figure(figsize=(7, 5))\n", "colors = plt.cm.viridis(np.linspace(0, 1, snaps))\n", "for i in range(snaps):\n", " plt.plot(xl, T_exact(xl, times[i], L, nu), color=colors[i], label=f\"Exact $t = {times[i]:.2f}$\")\n", " plt.plot(xl, T_snaps[i], \"s\", color=colors[i], lw=1, label=f\"LBM $t={(snaps_id[i]/nt)*t_end :.2f}$\",fillstyle='none')\n", " plt.plot(xl, Tf_snaps[i], \"o\", color=colors[i], lw=1, label=f\"FDM $t={(snaps_id[i]/nt)*t_end:.2f}$\",fillstyle='none')\n", "plt.xlabel(r\"$x$\",fontsize=18)\n", "plt.ylabel(r\"$\\phi(x,t)$\",fontsize=18)\n", "plt.legend()\n", "plt.xlim(0,1)\n", "plt.ylim(0,1.01)\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a8cd98fa-1ac0-412c-a58d-dbbe2b4c1dcb", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## 2nd Benchmark: Temperature ramp\n", "\n", "Analyzing the accuracy of diffusive equation solver, we apply it to a one-dimensional analytical case. The geometry is described by a domain of length $L$ initialized with a constant temperatura $T(x,t=0)=0$. The boundary conditions are given $T(x=0,t)=1$ and $T(x=L,t)=0$.\n", "\n", "### Steady-State Analytical Solution\n", "\n", "The analytical solution of this problem is given by:\n", "\n", "$$\n", "T(x,t\\rightarrow \\infty)= -\\frac{x}{L} + 1.\n", "$$\n", "\n", "### Transient Analytical Solution\n", "\n", "For the 1D heat equation $\\partial_t T=\\nu\\,\\partial_{xx}T$ on $0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "\n", "# ---- Modes and series -------------------------------------------------------\n", "def modes_dirichlet_dirichlet(L, N):\n", " n = np.arange(1, N+1) # n = 1,2,...,N\n", " k = n * np.pi / L # eigenvalues mu_n\n", " return n, k\n", "\n", "def project_coeffs_dirichlet(T0_func, L, N, grid_pts=4000):\n", " \"\"\"\n", " B_n = (2/L) ∫( T0(x) - T_ss(x) ) sin(nπx/L) dx, with T_ss = 1 - x/L.\n", " \"\"\"\n", " x = np.linspace(0.0, L, grid_pts, endpoint=True)\n", " Tss = 1.0 - x / L\n", " u0 = T0_func(x) - Tss\n", " n, k = modes_dirichlet_dirichlet(L, N) # (N,), (N,)\n", " S = np.sin(k[:, None] * x[None, :]) # (N, M)\n", " B = (2.0 / L) * np.trapz(u0[None, :] * S, x, axis=1)\n", " return B, n, k\n", "\n", "def T_series_dirichlet(x, t, L, nu, B, k):\n", " \"\"\"\n", " T(x,t) = T_ss(x) + sum_n B_n e^{-nu k_n^2 t} sin(k_n x), T_ss = 1 - x/L.\n", " \"\"\"\n", " x = np.asarray(x)\n", " Tss = 1.0 - x / L\n", " coeff = B * np.exp(-nu * (k**2) * t) # (N,)\n", " add = np.sum(coeff[:, None] * np.sin(k[:, None] * x[None, :]), axis=0)\n", " return Tss + add\n", "\n", "# ---- Parameters -------------------------------------------------------------\n", "L = 1.0\n", "nu = 0.1\n", "N = 200\n", "x = np.linspace(0, L, 600)\n", "\n", "# ---- Case A: initially cold rod T0(x)=0 (closed-form coefficients) ----------\n", "n, k = modes_dirichlet_dirichlet(L, N)\n", "B_cold = -2.0 / (n * np.pi) # exact coefficients for T0 ≡ 0\n", "\n", "times = [0.0, 0.01, 0.05, 0.2]\n", "\n", "plt.figure()\n", "for t in times:\n", " T_xt = T_series_dirichlet(x, t, L, nu, B_cold, k)\n", " plt.plot(x, T_xt, label=f\"$t = {t:g}$\")\n", "\n", "# steady state\n", "plt.plot(x, 1.0 - x/L, linestyle=\"--\", linewidth=1, label=\"steady state\")\n", "\n", "plt.xlabel(\"$x$\",fontsize=16)\n", "plt.ylabel(\"$T(x,t)$\",fontsize=16)\n", "plt.title(\"Heat eq.: $T(0,t)=1$, $T(L,t)=0$ ($T0(x)=0$)\")\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0587b233-3227-4251-a56e-3f3259b6224d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## 3rd Benchmark: Temperature Ramp with Adiabatic Boundary\n", "\n", "Assuming the **forward heat equation** in 1D with constant diffusivity $\\nu>0$,\n", "\n", "$$\n", "\\partial_t T=\\nu\\,\\partial_{xx}T,\\qquad 00,\n", "$$\n", "\n", "and the mixed boundary conditions\n", "\n", "$$\n", "T(0,t)=1,\\qquad \\partial_x T(L,t)=0,\n", "$$\n", "\n", "the steady state is $T_{\\mathrm{ss}}(x)=1$.\n", "\n", "Let $u(x,t)=T(x,t)-1$. Then $u$ solves\n", "\n", "$$\n", "\\partial_t u=\\nu\\,\\partial_{xx}u,\\quad u(0,t)=0,\\quad \\partial_x u(L,t)=0,\\quad u(x,0)=u_0(x):=T_0(x)-1.\n", "$$\n", "\n", "Separation of variables with eigenfunctions satisfying $X(0)=0,\\ X'(L)=0$ gives\n", "\n", "$$\n", "X_n(x)=\\sin(\\mu_n x),\\qquad \\mu_n=\\frac{(n+\\tfrac12)\\pi}{L},\\quad n=0,1,2,\\dots\n", "$$\n", "\n", "Hence the solution is the sine‐series\n", "\n", "$$\n", "\\boxed{\\\n", "T(x,t)=1+\\sum_{n=0}^{\\infty} A_n\\,e^{-\\nu\\,\\mu_n^{2}\\,t}\\,\\sin(\\mu_n x),\\qquad \n", "\\mu_n=\\frac{(n+\\tfrac12)\\pi}{L},\\\n", "}\n", "$$\n", "\n", "with coefficients (using $\\int_0^L \\sin(\\mu_m x)\\sin(\\mu_n x)\\,dx=\\tfrac{L}{2}\\delta_{mn}$)\n", "\n", "$$\n", "\\boxed{\\ A_n=\\frac{2}{L}\\int_0^L \\big[T_0(\\xi)-1\\big]\\sin(\\mu_n \\xi)\\,d\\xi.\\ }\n", "$$\n", "\n", "**Common special case (initially cold rod):** if $T_0(x)=0$, then $u_0(x)=-1$ and\n", "\n", "$$\n", "A_n=\\frac{2}{L}\\int_0^L (-1)\\sin(\\mu_n \\xi)\\,d\\xi=-\\frac{2}{L\\mu_n},\n", "$$\n", "\n", "so\n", "\n", "$$\n", "\\boxed{\\\n", "T(x,t)=1-\\sum_{n=0}^\\infty \\frac{2}{L\\mu_n}\\,e^{-\\nu\\,\\mu_n^{2}\\,t}\\,\\sin(\\mu_n x),\\qquad \n", "\\mu_n=\\frac{(n+\\tfrac12)\\pi}{L}.\\\n", "}\n", "$$\n", "\n", "> Note: if you literally use your original sign $\\partial_t T+\\nu T_{xx}=0$ (the **backward** heat equation), the time-dependent problem is ill-posed forward in $t$. For a physically meaningful diffusion process, use $\\partial_t T=\\nu T_{xx}$." ] }, { "cell_type": "code", "execution_count": 6, "id": "fa6705d3-815a-42fa-a985-d0e8bd7861fd", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "matplotlib.rcParams['mathtext.fontset'] = 'cm'\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "def heat_modes(L, N):\n", " n = np.arange(N)\n", " mu = (n + 0.5) * np.pi / L\n", " return mu\n", "\n", "def project_coeffs(T0_func, L, N, grid_pts=2000):\n", " x = np.linspace(0.0, L, grid_pts, endpoint=True)\n", " u0 = T0_func(x) - 1.0\n", " mu = heat_modes(L, N) # (N,)\n", " S = np.sin(mu[:, None] * x[None, :]) # (N, M)\n", " A = (2.0 / L) * np.trapz(u0[None, :] * S, x, axis=1) # (N,)\n", " return A, mu\n", "\n", "def T_series(x, t, L, nu, A, mu):\n", " x = np.asarray(x)\n", " coeff = A * np.exp(-nu * (mu**2) * t) # (N,)\n", " return 1.0 + np.sum(coeff[:, None] * np.sin(mu[:, None] * x[None, :]), axis=0)\n", "\n", "# ---- Parameters -------------------------------------------------------------\n", "L = 1.0\n", "nu = 0.1\n", "N = 200 # number of modes\n", "x = np.linspace(0, L, 600)\n", "\n", "# ---- Case 1: initially cold rod T0(x)=0 (closed-form A_n) -------------------\n", "mu = heat_modes(L, N)\n", "A_cold = -2.0 / (L * mu)\n", "\n", "times = [0.0, 0.01, 0.05, 0.2]\n", "\n", "plt.figure()\n", "for t in times:\n", " T_xt = T_series(x, t, L, nu, A_cold, mu)\n", " plt.plot(x, T_xt, label=f\"$t = {t:g}$\")\n", "\n", "# Steady-state baseline (T=1)\n", "plt.axhline(1.0, linestyle=\"--\", linewidth=1, label=\"steady state\")\n", "\n", "plt.xlabel(\"$x$\",fontsize=16)\n", "plt.ylabel(\"$T(x,t)$\",fontsize=16)\n", "plt.title(\"Heat eq. with $T(0,t)=1$, $T_x(L,t)=0$ (initially cold rod)\")\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "2a880a55-e243-4cef-86f5-60f5199a1dad", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [] } ], "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }