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Various numerical methods, including Finite Volume Method, Runge-Kutta 4 (RK4), Finite Difference Method, and Finite Element Method, have been implemented for accurate and efficient simulations.\n\n# Implemented Methods\n## Heat Equation\nThe heat equation describes the distribution of heat over time within a given region. I utilized the Finite Difference Method to discretize the partial differential equation and simulate the evolution of temperature. The RK4 method was employed for time integration, providing a stable and accurate solution.\n\n$$\n\\frac{\\partial C}{\\partial t} = D \\frac{\\partial^2 C}{\\partial x^2}\n$$\n\n$$\n\\frac{\\partial C}{\\partial x} = 0\n$$\n\n\n$$\n\\rho \\frac{dv}{dt} - \\mu \\left(\\frac{d^2 v}{dr^2} + \\frac{1}{r}\\frac{dv}{dr}\\right) = -\\nabla p\n$$\n\n\n$$\n\\rho C_p \\frac{\\partial T}{\\partial t} + \\rho C_p \\bar{v} \\cdot \\nabla T + \\nabla \\cdot \\left(-k \\nabla T\\right) = Q\n$$\n1. Numerical Method: Finite Difference Method\n2. Time Integration: Runge-Kutta 4 (RK4)\n# Wave Equation\nThe wave equation models the propagation of waves through a medium. Using the Finite Difference Method for spatial discretization and RK4 for time integration, I simulated the behavior of waves, showcasing the importance of accurate numerical methods in capturing wave dynamics.\n1. Numerical Method: Finite Difference Method\n2. Time Integration: Runge-Kutta 4 (RK4)\n#Heat Transfer\nHeat transfer is a critical aspect of many engineering applications. Implementing the Finite Volume Method allowed me to simulate heat transfer scenarios efficiently. This method discretizes the domain into control volumes, providing a robust approach for solving complex heat transfer problems.\n1. Numerical Method: Finite Volume Method\n# Finite Element Method\n1. Numerical Method: Finite Element Method\n\n##Contributions\nContributions are welcome! Feel free to submit issues or pull requests.\n\n##License\nThis project is licensed under the MIT License.\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fperpendicooler%2Fcomputational_fluid_dynamics","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fperpendicooler%2Fcomputational_fluid_dynamics","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fperpendicooler%2Fcomputational_fluid_dynamics/lists"}