Ansys Fluent allows you to choose one of the two numerical methods:
pressure-based solver (see Pressure-Based Solver)
density-based solver (see Density-Based Solver)
Historically speaking, the pressure-based approach was developed for low-speed incompressible flows, while the density-based approach was mainly used for high-speed compressible flows. However, recently both methods have been extended and reformulated to solve and operate for a wide range of flow conditions beyond their traditional or original intent.
In both methods the velocity field is obtained from the momentum equations. In the density-based approach, the continuity equation is used to obtain the density field while the pressure field is determined from the equation of state.
On the other hand, in the pressure-based approach, the pressure field is extracted by solving a pressure or pressure correction equation which is obtained by manipulating continuity and momentum equations.
Using either method, Ansys Fluent will solve the governing integral equations for the conservation of mass and momentum, and (when appropriate) for energy and other scalars such as turbulence and chemical species. In both cases a control-volume-based technique is used that consists of:
Division of the domain into discrete control volumes using a computational grid.
Integration of the governing equations on the individual control volumes to construct algebraic equations for the discrete dependent variables ("unknowns") such as velocities, pressure, temperature, and conserved scalars.
Linearization of the discretized equations and solution of the resultant linear equation system to yield updated values of the dependent variables.
The two numerical methods employ a similar discretization process (finite-volume), but the approach used to linearize and solve the discretized equations is different.
The general solution methods are described in Pressure-Based Solver and Density-Based Solver. To learn how to apply the solvers, see Choosing the Solver in the User's Guide.