{"id":24352677,"url":"https://github.com/victoorv/projet2_cpp","last_synced_at":"2026-05-21T00:33:22.348Z","repository":{"id":273001221,"uuid":"918431909","full_name":"VictoorV/Projet2_Cpp","owner":"VictoorV","description":"Résolution du problème de diffusion thermique en 2D dans un four.","archived":false,"fork":false,"pushed_at":"2025-01-17T23:40:59.000Z","size":123,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-01-18T00:24:49.918Z","etag":null,"topics":["2d","cpp","heat-equation","heat-equation-solution","numerical-analysis"],"latest_commit_sha":null,"homepage":"","language":"C++","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/VictoorV.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2025-01-17T23:24:40.000Z","updated_at":"2025-01-17T23:43:29.000Z","dependencies_parsed_at":"2025-01-18T00:35:50.425Z","dependency_job_id":null,"html_url":"https://github.com/VictoorV/Projet2_Cpp","commit_stats":null,"previous_names":["victoorv/projet2_cpp"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/VictoorV%2FProjet2_Cpp","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/VictoorV%2FProjet2_Cpp/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/VictoorV%2FProjet2_Cpp/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/VictoorV%2FProjet2_Cpp/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/VictoorV","download_url":"https://codeload.github.com/VictoorV/Projet2_Cpp/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":243165500,"owners_count":20246722,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["2d","cpp","heat-equation","heat-equation-solution","numerical-analysis"],"created_at":"2025-01-18T15:58:51.714Z","updated_at":"2025-12-27T02:19:37.854Z","avatar_url":"https://github.com/VictoorV.png","language":"C++","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Résolution du problème de diffusion thermique dans un four\n\nCe projet traite de la résolution du problème de diffusion thermique dans un four.  \nL'objectif est de **modéliser numériquement** le problème discrétisé par différences finies, puis de **résoudre le problème linéaire** $A \\mathbf{x} = \\mathbf{b}$ qui en découle.\n\n## Description du domaine étudié\n\nLe four est représenté par un domaine $\\Omega = ]0,1[^2$, avec :  \n- $\\partial \\Omega_D$ : les bords de Dirichlet.  \n- $\\partial \\Omega_N$ : les bords de Neumann.  \n\nL'objet dans le four est modélisé par le domaine $S = [0.25, 0.75] \\times [0.4, 0.6]$.  \nOn note $\\mathbf{n}$ le vecteur normal extérieur unitaire.\n\n## Équations du problème\n\nLa solution $T : \\Omega \\to \\mathbb{R}$ doit vérifier le système d'équations suivant :\n\n$$\n\\begin{cases}\n-\\text{div}(\\rho \\nabla T(x)) = 0, \u0026 \\forall x \\in \\Omega, \\\\\nT = T_D, \u0026 \\forall x \\in \\partial \\Omega_D, \\\\\n\\nabla T \\cdot \\mathbf{n} = 0, \u0026 \\forall x \\in \\partial \\Omega_N.\n\\end{cases}\n$$\n\n### Variables et notations\n- $T(x)$ : Température au point $x$.\n- $\\rho$ : Conductivité thermique (supposée constante ici).\n- $\\nabla T$ : Gradient de la température.\n- $\\text{div}$ : Divergence d'un champ vectoriel.\n- $\\mathbf{n}$ : Vecteur normal unitaire extérieur.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvictoorv%2Fprojet2_cpp","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fvictoorv%2Fprojet2_cpp","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvictoorv%2Fprojet2_cpp/lists"}