Publisher Summary This chapter focuses on computational fluid dynamics. For the flow of an incompressible fluid, if the Navier–Stokes equations of motion and the continuity equation are solved simultaneously under given boundary conditions, an exact solution should be obtained. However, because the Navier–Stokes equations are non-linear, it is difficult to solve them analytically. Nevertheless, approximate solutions are obtainable, for example, by omitting the inertia terms for a flow whose Re is small, such as slow flow around a sphere. For a compressible fluid, it is further necessary to solve the equation of state and the energy equation simultaneously with respect to the thermodynamical properties. Thus, multi-dimensional shockwave problems can only be solved by relying upon numerical solution methods. With the progress of computers, it has become popular to solve flow problems numerically. By such means it is possible to follow a kaleidoscopic change of flow. This field of engineering is referred to as numerical fluid mechanics or computational fluid dynamics. It can be roughly classified into four approaches: the finite difference method, the finite volume method, the finite element method, and the boundary element method. The chapter provides a discussion on these methods.