diff --git a/TP Physique Equation de la chaleur/TP Physique Equation de la chaleur.ipynb b/TP Physique Equation de la chaleur/TP Physique Equation de la chaleur.ipynb index f6976f2..abf5afa 100644 --- a/TP Physique Equation de la chaleur/TP Physique Equation de la chaleur.ipynb +++ b/TP Physique Equation de la chaleur/TP Physique Equation de la chaleur.ipynb @@ -10,40 +10,40 @@ "\n", "Eq en régime permanent\n", "\n", - "d2T / dx2 = 0\n", + "$\\frac{d^2T}{dx^2} = 0$\n", "\n", - "T(x =0) = T0\n", + "$T(x = 0) = T0$\n", "\n", - "T(x = 1) = T1\n", + "$T(x = 1) = T1$\n", "\n", - "T(i)i E [0, N+1]\n", + "$ T(i)_{i} \\in [0, N+1]$\n", "\n", - "x(i+1) - x(i) = deltaX = 1/N\n", + "$x(i+1) - x(i) = \\Delta X = \\frac{1}{N}$\n", "\n", - "d2T/dx2 = (T(i-1) - 2*T(i) + T(i+1))/deltaX**2\n", + "$\\frac{d2T}{dx2} = \\frac{T(i-1) - 2*T(i) + T(i+1)}{\\Delta x^2}$\n", "\n", "### Question 1: Résoudre cette équation pour les conditions aux bord\n", "$$\n", - "d2T / dx2 => dT / dx = A => T(x) = Ax + b\n", + "\\frac{d2T}{dx2} => \\frac{dT}{dx} = A => T(x) = Ax + b\n", "$$\n", "\n", - "Ici b = T0 d'où $$T(x) = Ax + T0$$\n", + "Ici $b = T0$ d'où $T(x) = Ax + T0$\n", "\n", "$$\n", - "T1 - T0 / 1 - 0 = A = T1 - T0 donc T(x) = (T1 - T0)x + T0\n", + "\\frac{T1 - T0}{1 - 0} = A = T1 - T0 donc T(x) = (T1 - T0)x + T0\n", "$$\n", - "### Question 2: Ecrire l'équation de la chaleur discrétisée pour i E [1, N-2], puis pour i = 0 et i = N\n", - "$$d2T/dx2 = 0$$\n", + "### Question 2: Ecrire l'équation de la chaleur discrétisée pour $i \\in [1, N-2]$, puis pour $i = 0$ et $i = N$\n", + "$$\\frac{d2T}{dx2} = 0$$\n", "\n", "$$T(i+1) - 2*T(i) + T(i-1) = 0$$\n", "\n", - "Pour i = 0: $$T(i-1) = ? => CB = T0-$$\n", + "Pour $i = 0$: $T(i-1) = ? => CB = T0-$\n", "\n", "$$\n", "-2T0 + T(1) = -T0-\n", "$$\n", "\n", - "Pour i = N: $$T(N+2) = T1+$$\n", + "Pour $i = N$: $T(N+2) = T1+$\n", "\n", "$$\n", "T(N) - 2T(N+1) = -T1+\n", @@ -61,10 +61,8 @@ "\\end{cases}\n", "$$\n", "\n", - "=> MT = b\n", - "\n", - "### Question 3: Montrer que l'équation discrétisée peut s'écrire: MT = b, avc M une matrice de taille N X N et b un vecteur de taille N. On précisera les termes non nuls de M et b.\n", - "Matrice du système (simplifiée pour N=6, normalement N indéfini)\n", + "### Question 3: Montrer que l'équation discrétisée peut s'écrire: $MT = b$, avc $M$ une matrice de taille $N * N$ et $b$ un vecteur de taille $N$. On précisera les termes non nuls de $M$ et $b$.\n", + "Matrice du système (simplifiée pour $N = 6$, normalement $N$ indéfini)\n", "$$\n", "\\begin{bmatrix}\n", "-2 & 1 & 0 & 0 & 0 & 0 & 0\\\\\n", @@ -96,16 +94,11 @@ "\\end{bmatrix}\n", "$$\n", "\n", - "### Question 4: Sous python, construire la matrice M et le vecteur b à l'aide de numpy. Résoudre ensuite le système linéaire à l'aide de la fonction numpy.linalg.solve(M, b).\n" + "### Question 4: Sous python, construire la matrice $M$ et le vecteur $b$ à l'aide de numpy. Résoudre ensuite le système linéaire à l'aide de la fonction numpy.linalg.solve(M, b).\n" ] }, { - "metadata": { - "ExecuteTime": { - "end_time": "2025-04-01T07:59:03.377422Z", - "start_time": "2025-04-01T07:59:03.319125Z" - } - }, + "metadata": {}, "cell_type": "code", "source": [ "import numpy as np\n", @@ -160,66 +153,26 @@ "plt.show()" ], "id": "d480d6e691bf7fbf", - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Matrice M: [[-2. 1. 0. ... 0. 0. 0.]\n", - " [ 1. -2. 1. ... 0. 0. 0.]\n", - " [ 0. 1. -2. ... 0. 0. 0.]\n", - " ...\n", - " [ 0. 0. 0. ... -2. 1. 0.]\n", - " [ 0. 0. 0. ... 1. -2. 1.]\n", - " [ 0. 0. 0. ... 0. 1. -2.]]\n", - "Matrice b: [ 4. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", - " 0. 0. -25.]\n", - "Solution T: [-3.71568627e+00 -3.43137255e+00 -3.14705882e+00 -2.86274510e+00\n", - " -2.57843137e+00 -2.29411765e+00 -2.00980392e+00 -1.72549020e+00\n", - " -1.44117647e+00 -1.15686275e+00 -8.72549020e-01 -5.88235294e-01\n", - " -3.03921569e-01 -1.96078431e-02 2.64705882e-01 5.49019608e-01\n", - " 8.33333333e-01 1.11764706e+00 1.40196078e+00 1.68627451e+00\n", - " 1.97058824e+00 2.25490196e+00 2.53921569e+00 2.82352941e+00\n", - " 3.10784314e+00 3.39215686e+00 3.67647059e+00 3.96078431e+00\n", - " 4.24509804e+00 4.52941176e+00 4.81372549e+00 5.09803922e+00\n", - " 5.38235294e+00 5.66666667e+00 5.95098039e+00 6.23529412e+00\n", - " 6.51960784e+00 6.80392157e+00 7.08823529e+00 7.37254902e+00\n", - " 7.65686275e+00 7.94117647e+00 8.22549020e+00 8.50980392e+00\n", - " 8.79411765e+00 9.07843137e+00 9.36274510e+00 9.64705882e+00\n", - " 9.93137255e+00 1.02156863e+01 1.05000000e+01 1.07843137e+01\n", - " 1.10686275e+01 1.13529412e+01 1.16372549e+01 1.19215686e+01\n", - " 1.22058824e+01 1.24901961e+01 1.27745098e+01 1.30588235e+01\n", - " 1.33431373e+01 1.36274510e+01 1.39117647e+01 1.41960784e+01\n", - " 1.44803922e+01 1.47647059e+01 1.50490196e+01 1.53333333e+01\n", - " 1.56176471e+01 1.59019608e+01 1.61862745e+01 1.64705882e+01\n", - " 1.67549020e+01 1.70392157e+01 1.73235294e+01 1.76078431e+01\n", - " 1.78921569e+01 1.81764706e+01 1.84607843e+01 1.87450980e+01\n", - " 1.90294118e+01 1.93137255e+01 1.95980392e+01 1.98823529e+01\n", - " 2.01666667e+01 2.04509804e+01 2.07352941e+01 2.10196078e+01\n", - " 2.13039216e+01 2.15882353e+01 2.18725490e+01 2.21568627e+01\n", - " 2.24411765e+01 2.27254902e+01 2.30098039e+01 2.32941176e+01\n", - " 2.35784314e+01 2.38627451e+01 2.41470588e+01 2.44313725e+01\n", - " 2.47156863e+01]\n" - ] - }, - { - "data": { - "text/plain": [ - "
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" - }, - "metadata": {}, - "output_type": "display_data" - } + "outputs": [], + "execution_count": null + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "## Exercice 3\n", + "$$\n", + "\\frac{dT}{dt} = D \\frac{d^2T}{dx^2}\n", + "$$\n", + "Le coefficient de diffusion $D$ sera pris égal à 1.\n", + "### Question 1: Rappeler l'itération d'Euler pour la dérivée première et pour un pas de temps $dt$.\n", + "On se place au temps $n$ pour un certain $i$:\n", + "$$\n", + "\\frac{T^{n+1}_{i} - T^n_{i}}{\\Delta t} = D \\frac{T^{n}_{i-1} - 2T^n_{i} + T^{n}_{i+1}}{\\Delta x^2}\n", + "$$\n", + "\n" ], - "execution_count": 9 + "id": "24aae10ae7862f9c" } ], "metadata": {