The Finite Volume Method

This lecture introduces the Finite Volume Method (FVM) for numerical flow simulation. It covers the governing equations for incompressible and compressible flows, conservation equations, model equations, and the application of FVM to solve steady diffusion and convection-diffusion problems. The lecture explains the discretization of unknowns, volume and surface integrals, and boundary conditions. It also discusses the FVM in 1D examples, including heat conduction, and various interpolation methods for surface integrals. Additionally, it explores local and global conservation, the transformation of PDEs into algebraic equations, and the division of domains into control volumes.