A set of numerical methods and algorithms used to solve and analyse problems involving complex fluid flow behaviour. The problems require many computations that are required to be performed simultaneously using high-speed computers. The problems involve the simulation of the interaction of liquids and gases with surfaces defined by boundary conditions. The Navier–Stokes equations are used to define most CFD problems involving a single phase as a liquid or a gas, but not both. For problems involving fluid mechanics, the solvers are based on the finite volume method. For 2-D or 3-D problems, the geometry of interest is first defined as an area or volume and divided into discrete control volumes or cells known as a mesh. The flow into these cells obeys the general laws of conservation for mass, momentum, and energy as algebraic equations. The boundary conditions are specified and in the case of problems involving transient behaviour, the initial conditions are also defined. All the equations are then solved iteratively. The solution is then presented for visual analysis and interpretation. There have been many developments in CFD methodologies and many are available as commercial software packages that can be applied to the study of complex fluid flow systems.