Chapter 30 - Finite difference method

Abstract

Having covered the fundamentals of the Galerkin method, we will now turn to the so-called finite difference method. This method is directly derived from the Taylor series expansion and constitutes one of the most exact numerical methods available. As we will see, the main disadvantage of finite difference schemes is their limited geometric flexibility and high numerical cost. However, they are easy to implement and we will use these schemes at a later point in time to implement a custom-written three-dimensional numerical solver. In this section, we will use Microsoft Excel to find numerical solutions to rather complex flow cases.