Computational fluid dynamics (CFD) is the use of computers to analyze 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. Where shocks or discontinuities are present, high resolution, total variation diminishing numerical schemes are needed to avoid spurious oscillations in the solution. 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 mesh-based method, a number of alternatives exist, notably :

• smoothed particle hydrodynamics, a Lagrangian method of solving fluid problems,
• Spectral methods, a technique where the equations are projected onto basis functions like the spherical harmonics and Chebyshev polynomials
• Lattice Boltzmann methods, which simulate an equivalent mesoscopic system on a Cartesian grid, instead of solving the macroscopic system (or the real microscopic physics).

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 (such as blood).

Methodology

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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.

Discretization methods

The stability of the chosen discretization is generally established numerically rather than analytically as with simple linear problems. Special care must also be taken to ensure that the discretization handles discontinuous solutions gracefully. The Euler equations and Navier-Stokes equations both admit shocks, and contact surfaces.

Some of the discretization methods being used are:

• Finite volume method. This is 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):

$\backslash frac\{\backslash partial\}\{\backslash partial\; t\}\backslash iiint\; Q\; dV\; +\; \backslash iint\; F\; d\backslash mathbf\{A\}\; =\; 0,$

Where $Q$ is the vector of conserved variables, $F$ is the vector of fluxes (see Euler equations or Navier-Stokes equations), $V$ is the cell volume, and $\backslash mathbf\{A\}$ is the cell surface area.

• 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 method. This method has historical importance and is simple to program. It is currently only used in few specialized codes. Modern finite difference codes make use of an embedded boundary for handling complex geometries making these codes highly efficient and accurate. Other ways to handle geometries are using overlapping-grids, where the solution is interpolated across each grid.

$$

\frac{\partial Q}{\partial t}+ \frac{\partial F}{\partial x}+ \frac{\partial G}{\partial y}+ \frac{\partial H}{\partial z}=0

Where $Q$ is the vector of conserved variables, and $F$, $G$, and $H$ are the fluxes in the $x$, $y$, and $z$ directions respectively.

• Boundary element method. The boundary occupied by the fluid is divided into surface mesh.
• High resolution schemes are used where shocks or discontinuities are present. To capture sharp changes in the solution requires the use of second or higher order numerical schemes that do not introduce spurious oscillations. This usually necesitates the application of flux limiters to ensure that the solution is total variation diminishing.

Turbulence models

Direct numerical simulation

Direct numerical simulation (DNS) captures all of the relevant scales of turbulent motion, so no model is needed for the smallest scales. This approach is extremely expensive, if not intractable, for complex problems on modern computing machines, hence the need for models to represent the smallest scales of fluid motion.

Reynolds-averaged Navier-Stokes

Reynolds-averaged Navier-Stokes equations (RANS) is the oldest approach to turbulence modeling. An ensemble version of the governing equations is solved, which introduces new apparent stresses known as Reynolds stress. This adds a second order tensor of unknowns for which various models can provide different levels of closure. It is a common misconception that the RANS equations do not apply to flows with a time-varying mean flow because these equations are 'time-averaged'. In fact, statistically unsteady (or non-stationary) flows can equally be treated. This is sometimes referred to as URANS. There is nothing inherent in Reynolds averaging to preclude this, but the turbulence models used to close the equations are valid only as long as the time over which these changes in the mean occur is large compared to the time scales of the turbulent motion containing most of the energy.

Large eddy simulation

Large eddy simulations (LES) is a technique in which the smaller eddies are filtered and are modeled using a sub-grid scale model, while the larger energy carrying eddies are simulated. This method generally requires a more refined mesh than a RANS model, but a far coarser mesh than a DNS solution.

Detached eddy simulation

Detached eddy simulations (DES) is a modification of a RANS model in which the model switches to a subgrid scale formulation in regions fine enough for LES calculations. Regions near solid boundaries and where the turbulent length scale is less than the maximum grid dimension are assigned the RANS mode of solution. As the turbulent length scale exceeds the grid dimension, the regions are solved using the LES mode. Therefore the grid resolution is not as demanding as pure LES, thereby considerably cutting down the cost of the computation. Though DES was initially formulated for the Spalart-Allmaras model (Spalart et al, 1997), it can be implemented with other RANS models (Strelets, 2001), by appropriately modifying the length scale which is explicitly or implicitly involved in the RANS model. So while Spalart-Allamaras model based DES acts as LES with a wall model, DES based on other models (like two equation models) behave as a hybrid RANS-LES model. Grid generation is more complicated than for a simple RANS or LES case due to the RANS-LES switch. DES is a non-zonal approach and provides a single smooth velocity field across the RANS and the LES regions of the solutions.

Solution algorithms

The basic solution of the system of equations arising after discretization is accomplished by many of the familiar algorithms of numerical linear algebra. One can either use a stationary iterative method, like symmetric Gauss-Seidel or successive overrelaxation, or a Krylov subspace method. In the latter, the solution residual is minimized on an orthogonal basis for a subspace of the non-linear operator. Krylov subspace methods are generally used with a preconditioner and an inner Newton iteration. Unfortunately for non-linear problems, the orthogonal basis can not be constructed with short recurrences (as in the plain conjugate gradient method) and the entire sequence of vectors must be stored.
In recent years so-called Multigrid algorithms have become very popular, because of their efficiency for larger systems of equation, i.e. finer discretization meshes. This technique avoids the disadvantage of the above mentioned iterative solvers, that information travels slowly from one point of the grid to another by changing to coarser grids and later interpolating back to the fine grid.

Motivation

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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, CFD-ACE+,CFD-FASTRAN by ESI GROUP, EFD.Lab, CFX by ANSYS Inc., Coolit, FLOW-3D, FLUENT, KIVA, NUMECA, Phoenics, STAR-CD by CD-adapco. Other software packages serve as add-ons or complementary products to CFD tools. These include FIELDVIEW or Tecplot for post-processing and KINetics for solving detailed chemical kinetics.

The major problem faced by the CFD industry today is a shortage of skilled human resource. CFD development requires blend of technologist and programmer. Likewise CFD analysis needs good insight in the physics of the problem, understanding of numerical methods used along with expertise in commercial CFD software packages. In India, Centre for Computational Technologies (CCTech) provides professional training to fresh engineering graduates and working professionals.

Software

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• OpenFOAM a former commercial code that is now under GPL
• OpenFlower an easy to use 3-D and 2-D flow solver. It is open source and has both, a dummies guide and a manual of how and what it solves. Use it for preliminary CFD before you go fluent. Use GMSH for your models, solve them using OpenFlower, then view the results using GMSH again. export stl from Pro/e - SW soon? GMSH
• FLUENT World's most widely used commercial CFD code for a wide range of industrial flow applications
• STAR-CD Previously the most used CFD code in the Automotive industry (now replaced by FLUENT), also strong useage across industries. Reputation for polyhedral meshing and Computational Continuum Mechanics
• HyperXtrude Commercial CFD code for metal extrusion and similar problems (polymers, toothpaste, clay, Italian pasta ...)
• CFX Popular CFD-code embedded in the Ansys Workbench environment
• CFdesign CFdesign® turns a standard MCAD workstation into a fully interactive flow bench, thermal test rig, and wind tunnel, using a Finite Element technique.
• GOTM General Ocean Turbulence Model, freely available, published under GPL.
• GETM GETM is a 3D numerical model simulating the most important hydrodynamic and thermodynamic processes in natural waters, freely available, published under GPL.
• MultiSurface Aerodynamics Wing Analysis Software using Vortex Lattice CFD method.
• Dolfyn an Open Source unstructured Finite Volume Method code
• Edge Unstructured Finite-Volume CFD-code from FOI featuring DES, LES, aeroelasticity, shape optimization (adjoint solver). Binaries are freely distributed.
• MFIX is an open source multiphase CFD software developed at NETL.
• NIKA EFD.Lab
• NASA provides CFD software to residents in the US through The Open Channel Foundation
• GERRIS is a GPL incompressible flow solver
• Featflow is an Open Source 2-D and 3-D Finite Element Method incompressible flow solver
• Femwater is a freely downloadable(including source) finite element code developed by the EPA to calculate chemical transport through fluids. The EPA site does not include source code(use previous link) but it does provide an executable as well as a description of Femwater.
• Typhon is an open source multiphysics solver (includes compressible flow and heat transfer)
• Piping Systems FluidFlow has a fully functional demo which uses sample fluids for evaluations available for download
• Atmos
• WANDA WL|Delft Hydraulics transient flow simulation of pipeline networks, including extensive boundary conditions (pumps, valves, etc.), water hammer, free surface flow and control simulation
• Stoner Pipeline Simulator transient flow simulation of natural gas or oil transmission systems
• SynerGEE general purpose-modeling tool for piping networks including natural gas and water
• PipelineStudio Steady-state and transient flow simulation for gas or liquid pipeline networks, evaluation download available (~ 132 M)
• Olga 2000
• CFD Studio Educational program to study CFD Problems
• Hysys
• Comet commercial Finite Volume Method
• Channelflow Channelflow uses "spectral method" (GPL)
• Net-Pipe
• NEKTON "Spectral Element Method (SEM)"
• PowerFLOW from Exa Commercial "Lattice Boltzmann Method" for high Reynolds number, low Mach number flows
• 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
• Daat Research Corp. makers Coolit and CoolitPCB CFD software for electronics cooling applications
• CFD-ACE+ CFD code for wide range of multiphysics applications
• CFD-FASTRAN CFD code for aerodynamic/aerospace applications
• CFD-CADalyzer CFD code for simulation based design (links with CAD)
• FLOW-3D CFD code especially for free surface flow applications
• ICEM CFD Engineering - Involved in various CFD products mainly Mesh Generation products like ICEMCFD HEXA. Acquired by ANSYS Inc. in 1998.
• FIELDVIEW™ commercial post-processing and visualization for commercial and proprietary CFD solver data from Intelligent Light. Includes interrogation, animation, presentation, and collaboration tools. Free trial software available.
• Tecplot CFD post-processing, plotting, graphing and visualization software.
• COSILAB - software and CFD add-ins for chemistry in laminar and turbulent flows
• Reaction Design - software for chemical kinetics and CFD add-ins
• FLOTHERM commercial CFD software with for electronics cooling, from Flomerics
• FLOVENT commercial CFD software for the built environment, from Flomerics
• FLOPCB collaborative design software for conceptual PCB design by product marketing, electrical and mechanical engineers, from Flomerics
• COMSOL Multiphysics (aka FEMLAB) commercial finite element package for multiphysics including CFD
• TAU Unstructured Finite-Volume CFD-code from DLR for aircraft and rotorcraft
• FLOWer Structured Finite-Volume CFD-code from DLR for aircraft and rotorcraft
• Moldex3D commercial CAE software for injection molding
• Pointwise - makers of Gridgen
• Metacomp Technologies, Inc. - makers of CFD++
• Tdyn is a fluid dynamic (CFD) simulation environment based on the stabilized Finite Element Method
• NIST Fire Dynamics Simulator (FDS)is a CFD model for low-speed, thermally-driven fluid flow with an emphasis on smoke and heat transport from fires
• GRUMMP is a 2D and 3D unstructured mesh generation and refinement software
• PASSAGE Software by Technalysis Passage® software is a collection of 3D and 1D finite element programs solving complex flow, heat transfer and other related problems in product design and manufacturing
• Moldflow Plastics Insight - Plastics flow analysis software
• PHOENICS CFD from CHAM - 3D, time dependent Navier-Stokes finite volume solver. First commercial solver, still being extended. Shareware older versions available.
• ZEUS Numerix Located at the Technology Business Incubator of the Indian Institute of Technology (Bombay), the Zeus group has developed CFDExpert & Tutor, GridZ & FlowZ

External links

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• CFDWiki
• http://openflower.sourceforge.net
• http://www.cfdnet.ca
• http://www.cfd-online.com
• http://www.cfdreview.com
• http://www.cavityflow.com (Dead Link)
• Usenet discussion group on CFD
• http://www.tridiagonal.co.in

See also

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• Blade element theory

Fluid dynamics

Numerische Strömungsmechanik | دینامیک محاسباتی سیالات | Computational fluid dynamics | CFD | Fluidodinamica computazionale | CFD | 计算流体力学