Finite Volume Method for Heat Transfer Simulation

This documentation presents a MATLAB program implementing the Finite Volume Method (FVM) for solving heat transfer problems. In thermal engineering, FVM serves as a fundamental numerical approach for discretizing and solving heat conduction equations. The method's primary advantages include accurate thermal modeling capabilities and flexible handling of diverse boundary conditions. The MATLAB implementation systematically executes the FVM workflow through four key computational phases: 1. Mesh Generation: Constructs structured/unstructured grids using MATLAB's mesh generation functions (e.g., meshgrid for 2D or generateMesh for 3D geometries). The code defines control volumes and calculates geometric parameters like cell centroids and face areas. 2. Boundary Condition Implementation: Configures thermal constraints through dedicated functions handling Dirichlet (fixed temperature), Neumann (heat flux), and convective boundary conditions. The program uses logical indexing to identify boundary nodes and applies corresponding discretization schemes. 3. Coefficient Matrix Assembly: Builds the sparse coefficient matrix representing discretized heat equations. The implementation employs central differencing for diffusion terms and upwind schemes for convective components, ensuring conservation through flux balancing across cell interfaces. 4. Linear System Solution: Utilizes iterative solvers (e.g., Gauss-Seidel or built-in backslash operator for direct methods) to compute temperature distribution. The code includes convergence monitoring with residual checks and optional preconditioning for large-scale problems. This MATLAB toolkit provides a practical framework for analyzing diverse thermal phenomena including pure conduction, coupled convection-diffusion, and transient heat transfer. Through modular code architecture and detailed comments, users can extend the base implementation to address complex engineering scenarios while deepening their understanding of FVM fundamentals.