Computational fluid dynamics
Computational fluid dynamics is the use of computers to analyse problems in fluid dynamics.
The usual method is to discretize the fluid domain into small cells to form a volume mesh or grid, and then apply iterative methods to solve the equations of motion (aka the Navier-Stokes equations) for them.
While it is possible to directly solve the Navier-Stokes equations for laminar flow cases, turbulent flows require the introduction of a turbulence model. The RANS formulation (Reynolds-averaged Navier-Stokes equations) is the usual modelling technique used, with the two equation k-e model
being the most common form of closure in industrial use.
In many instances, other equations (mostly convective-diffusion equations) are solved simultaneously with the Navier-Stokes equations.
These other equations can include those describing species concentration, chemical reactions, heat transfer, etc.
More advanced codes allow the simulation of more complex cases involving multi-phase flows (eg, liquid/gas, solid/gas, liquid/solid) or non-Newtonian fluids.
The discretization methods:
- finite volume method The "classical" or standard approach used most often in commercial sofware and research codes. The governing equations are solved on discrete control volumes. This integral approach yields a method that is inherently convervative (i.e., quantities such as density remain physically meaningful).
- finite element method This method is popular for structural analysis of solids, but also has applicable to fluids. The FEM formulation requires, however, special care to ensure a conservative solution.
- finite difference This method has historical importance and is simple to program. It is currently only used in few specialized codes.
In all of these approaches the same basic procedure is followed.
- The geometry (physical bounds) of the problem is defined.
- The volume occupied by the fluid is divided into discrete cells (the mesh).
- The physical modelling is defined - for example, the equations of motions + enthalpy + species conservation
- Boundary conditions are defined. This involves specifying the fluid behaviour and properties at the boundaries of the problem. For transient problems, the initial conditions are also defined.
- The equations are solved iteratively as a steady-state or transient.
- Analysis and visualization of the resulting solution.
The techniques are widely used by engineers designing or analysing devices that interact with fluid, such as vehicles, pumps, chemical apparatus or ventilation systems.
There are numerous commercial software packages to solve the Navier Stokes Equations. Examples of such commercial packages include the following (alphabetically listed):
AVL/FIRE, CFX, Fluent, FOAM, KIVA, NUMECA,
