In this project you will solve the steady and unsteady 2D heat conduction equations. You will implement explicit and implicit approaches for the unsteady case and learn the differences between them. You will also learn how to implement iterative solvers like Jacobi, Gauss-Seidel and SOR for solving implicit equations.
Step 1 - Setting up the mesh and initial/boundary conditions
Step 2 - Implement steady/unsteady solution using Explicit and Implicit approaches
Step 3 - Perform convergence rate study
Step 4 - Perform stability analysis
In this project, you will create a 2D solver to simulate the 2D Heat Conduction equation. You will solve both the steady and unsteady governing equations and implement the Explicit and Implicit approaches to solving the transient problem. The implicit equations will be solved using the iterative solvers like Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR). You will then perform the convergence study among all the implemented approaches and finally carry out stability analysis for explicit and implicit approaches.
Diffusion is an important phenomena that occurs in fluid flow. The Navier-Stokes equation contains a diffusion term. So it is essential to understand how to discretize and simulate such phenomena in order to gain deeper insights into the Navier-Stokes equation. And in this project you do exactly that. You take up a diffusion problem such as the 2D heat conduction and learn how to solve the steady and unsteady forms of the equation by employing Finite Difference method. You will learn to implement the explicit and implicit approaches for transient simulation. You will also learn how to implement iterative solvers to solve simultaneous equations that arise in steady and transient implicit approaches. You will then perform a convergence study on the iterative solvers and conduct a stability analysis for implicit and explicit solutions.
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