Computational fluid dynamics



Computational fluid dynamics (CFD) is the use of computers to analyse problems in fluid dynamics.

The most fundamental consideration in CFD is how one treats a continuous fluid in a discretized fashion on a computer. One method is to discretize the spatial domain into small cells to form a volume mesh or grid, and then apply a suitable algorithm to solve the equations of motion (Euler equations for inviscid, and Navier-Stokes equations for viscid flow). In addition, such a mesh can be either irregular (for instance consisting of triangles in 2D, or pyramidal solids in 3D) or regular; the distinguishing characteristic of the former is that each cell must be stored separately in memory. Lastly, if the problem is highly dynamic and occupies a wide range of scales, the grid itself can be dynamically modified in time, as in adaptive mesh refinement methods.

If one chooses not to proceed with a grid-based method, a number of alternatives exist, notably :

It is possible to directly solve the Navier-Stokes equations for laminar flow cases and for turbulent flows when all of the relevant length scales can be contained on the grid (a direct numerical simulation). In general however, the range of length scales appropriate to the problem is larger than even today's massively parallel computers can model. In these cases, turbulent flow simulations require the introduction of a turbulence model. large eddy simulations and the RANS formulation (Reynolds-averaged Navier-Stokes equations), with the k-ε model or the Reynolds stress model, are two techniques for dealing with these scales.

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 software and research codes. The governing equations are solved on discrete control volumes. This integral approach yields a method that is inherently conservative (i.e., quantities such as density remain physically meaningful).
  • finite element method This method is popular for structural analysis of solids, but is also 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.
  • boundary element method The boundary occupied by the fluid is divided into surface mesh.

In all of these approaches the same basic procedure is followed.

  1. The geometry (physical bounds) of the problem is defined.
  2. The volume occupied by the fluid is divided into discrete cells (the mesh).
  3. The physical modelling is defined - for example, the equations of motions + enthalpy + species conservation
  4. 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.
  5. The equations are solved iteratively as a steady-state or transient.
  6. 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, KIVA, NUMECA, Phoenics, and STAR-CD. Other software packages serve as add-ons or complementary products to CFD tools. These include FieldView for post-processing and KINetics for solving detailed chemical kinetics.

External links



  • OpenFOAM ( a former commercial code that is now under GPL
  • NASA ( provides CFD software to residents in the US
  • GERRIS ( is a GPL incompressible flow solver
  • Piping Systems FluidFlow ( has a fully functional demo which uses sample fluids for evaluations available for download
  • Atmos (
  • Stoner Pipeline Simulator (
  • Pipeline Studio ( includes an evaluation download (~ 132 M)
  • Olga 2000 (
  • Hysys (
  • Channelflow ( Channelflow uses "spectral method" (GPL)
  • Net-Pipe (
  • Exa ( Powerflow "Lattice Boltzmann Method"
  • Enzo ( is an open-source cosmological simulation code that uses an adaptive mesh.
  • FLASH ( is a free for non-commercial use, adaptive mesh, compressible solver for astrophysical flows
  • STAR ( Industrial CAD-embedded flow simulation
  • FLUENT ( CFD code for a wide range of flow modeling applications
  • Intelligent Light ( - makers of FieldView
  • TecPlot ( CFD post-processing, plotting, graphing and visualization software.
  • Reaction Design ( - software for chemical kinetics and CFD add-ins
  • Flotherm ( commercial CFD software with emphasis on electronic enclosures, cartesian grid
  • FEMLAB ( commercial finite element package for multi-physics including CFD
  • CFX ( CFD-code by Ansys
  • TAU ( Unstructured Finite-Volume CFD-code from DLR for aircraft and rotorcraft
  • FLOWer ( Structured Finite-Volume CFD-code from DLR for aircraft and rotorcraftde:Numerische Strmungssimulation

it:Fluidodinamica computazionale zh:计算流体力学


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