A computer simulation of high velocity air flow around the Space Shuttle during re-entry.

Computational fluid dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the millions of calculations required to simulate the interaction of fluids and gases with the complex surfaces used in engineering. However, even with simplified equations and high-speed supercomputers, only approximate solutions can be achieved in many cases. More accurate codes that can accurately and quickly simulate even complex scenarios such as transonic or turbulent flows are an ongoing area of research. Validation of such codes is often performed using a wind tunnel. Image File history File linksMetadata CFD_Shuttle. ... Image File history File linksMetadata CFD_Shuttle. ... NASAs Space Shuttle, officially called Space Transportation System (STS), is the United States governments current manned launch vehicle. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ... Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). ... A supercomputer is a computer that leads the world in terms of processing capacity, particularly speed of calculation, at the time of its introduction. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... NASA wind tunnel with the model of a plane A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects. ...

Background and history

A simulation of the Hyper-X scramjet vehicle in operation at Mach-7

The fundamental basis of any CFD problem is the Navier-Stokes equations, which define any single-phase fluid flow. These equations can be simplified by removing terms describing viscosity to yield the Euler equations. Further simplification, by removing terms describing vorticity yields the full potential equations. Finally, these equations can be linearized to yield the linearized potential equations. Image File history File links Download high-resolution version (3030x2606, 2081 KB) Hyper - X at Mach 7: This computational fluid dynamic (CFD) image is of the Hyper - X at the Mach 7 test condition with the engine operating. ... Image File history File links Download high-resolution version (3030x2606, 2081 KB) Hyper - X at Mach 7: This computational fluid dynamic (CFD) image is of the Hyper - X at the Mach 7 test condition with the engine operating. ... Hyper-X is a NASA multi-year experimental hypersonic ground and flight test program. ... An F/A-18 Hornet breaking the sound barrier. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ... In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. ...

Historically, methods were first developed to solve the Linearized Potential equations. Two-dimensional methods, using conformal transformations of the flow about a cylinder to the flow about an airfoil were developed in the 1930s. The computer power available paced development of three-dimensional methods. The first paper on a practical three-dimensional method to solve the linearized potential equations was published by John Hess and A.M.O. Smith of Douglas Aircraft in 1966. This method discretized the surface of the geometry with panels, giving rise to this class of programs being called Panel Methods. Their method itself was simplified, in that it did not include lifting flows and hence was mainly applied to ship hulls and aircraft fuselages. The first lifting Panel Code (A230) was described in a paper written by Paul Rubbert and Gary Saaris of Boeing Aircraft in 1968. In time, more advanced three-dimensional Panel Codes were developed at Boeing (PANAIR, A502), Lockheed (Quadpan), Douglas (HESS), McDonnell Aircraft (MACAERO), NASA(PMARC) and Analytical Methods (WBAERO, USAERO and VSAERO). Some (PANAIR, HESS and MACAERO) were higher order codes, using higher order distributions of surface singularities, while others (Quadpan, PMARC, USAERO and VSAERO) used single singularities on each surface panel. The advantage of the lower order codes was that they ran much faster on the computers of the time. Today, VSAERO has grown to be a multi-order code and is the most widely used program of this class. This program has been used in the development of many submarines, surface ships, automobiles, helicopters and aircraft. Its sister code, USAERO is an unsteady panel method that has also been used for modeling such things as high speed trains and racing yachts. The NASA PMARC code was developed from an early version of VSAERO and a derivative of PMARC, named CMARC, is also commercially available. Look up cylinder in Wiktionary, the free dictionary. ... Various components of the airfoil. ... The 1930s (years from 1930–1939) were described as an abrupt shift to more radical and conservative lifestyles, as countries were struggling to find a solution to the Great Depression, also known in Europe as the World Depression. ... The space we live in is three-dimensional space. ... Apollo Milton Olin Smith (usually referred to as A.M.O. Smith)(July 2, 1911 – February 2, 1997) was an important figure in the aerodynamics field at Douglas Aircraft from 1938 to 1975 and an early pioneer in the area of Computational Fluid Dynamics. ... The Douglas Aircraft Company was founded by Donald Wills Douglas in July 1921. ... 1966 (MCMLXVI) was a common year starting on Saturday (the link is to a full 1966 calendar). ... 1968 (MCMLXVIII) was a leap year starting on Monday. ... The Boeing Company (NYSE: BA, TYO: 7661 ) is an aerospace and defense corporation headquartered in Chicago, Illinois. ... The Lockheed SR-71, remarkably advanced for its time and unsurpassed in many areas of performance The Lockheed U-2 first flew in 1955 providing much needed intelligence on Soviet bloc countries Lockheed Corporation was an aerospace company founded in 1912 which merged with Martin Marietta in 1995 to form... The Douglas Aircraft Company was founded by Donald Wills Douglas, Sr. ... The McDonnell Aircraft Corporation was an American aerospace manufacturer, based near St. ... The National Aeronautics and Space Administration (NASA) is an agency of the United States Government, responsible for the nations public space program. ... German UC-1 class World War I submarine A model of Günther Priens Unterseeboot 47 (U-47), German WWII Type VII diesel-electric hunter Typhoon class nuclear ballistic missile submarine USS Virginia, a Virginia-class nuclear attack (SSN) submarine A submarine is a watercraft that can operate underwater... Italian Full rigged ship Amerigo Vespucci in New York Harbor, 1976 A ship is a large watercraft capable of deep water navigation. ... Karl Benzs Velo (vélo means bicycle in French) model (1894) - entered into the first automobile race 2005 MINI Cooper S. An automobile (also motor car or simply car) is a wheeled passenger vehicle that carries its own motor. ... A helicopter is an aircraft which is lifted and propelled by one or more horizontal rotors consisting of two or more rotor blades. ... Look up aircraft in Wiktionary, the free dictionary. ... A modern yacht A yacht (From Dutch Jacht meaning hunt) pron. ...

In the two-dimensional realm, quite a number of Panel Codes have been developed for airfoil analysis and design. These codes typically have a boundary layer analysis included, so that viscous effects can be modeled. Professor Richard Eppler of the University of Stuttgart developed the PROFIL code, partly with NASA funding, which became available in the early 1980s. This was soon followed by MIT Professor Mark Drela's Xfoil code. Both PROFIL and Xfoil incorporate two-dimensional panel codes, with coupled boundary layer codes for airfoil analysis work. PROFIL uses a conformal transformation method for inverse airfoil design, while Xfoil has both a conformal transformation and an inverse panel method for airfoil design. Both codes are widely used. In physics and fluid mechanics, the boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... The Universität Stuttgart is the University of Stuttgart. ... The 1980s refers to the years of and between 1980 and 1989. ... Mapúa Institute of Technology (MIT, MapúaTech or simply Mapúa) is a private, non-sectarian, Filipino tertiary institute located in Intramuros, Manila. ... In mathematics and theoretical physics, a conformal transformation is a transformation of coordinates that preserves the angle. ...

An intermediate step between Panel Codes and Full Potential codes were codes that used the Transonic Small Disturbance equations. In particular, the three-dimensional WIBCO code, developed by Charlie Boppe of Grumman Aircraft in the early 1980s has seen heavy use. The Grumman Aircraft Engineering Corporation, later Grumman Aerospace Corporation, was a leading producer of military and civilian aircraft of the 20th century. ...

Developers next turned to Full Potential codes, as panel methods could not calculate the non-linear flow present at transonic speeds. The first description of a means of using the Full Potential equations was published by Earll Murman and Julian Cole of Boeing in 1970. Frances Bauer, Paul Garabedian and David Korn of the Courant Institute at New York University (NYU) wrote a series of two-dimensional Full Potential airfoil codes that were widely used, the most important being named Program H. A further growth of Progam H was developed by Bob Melnik and his group at Grumman Aerospace as Grumfoil. Antony Jameson, originally at Grumman Aircraft and the Courant Institute of NYU, worked with David Caughey to develop the important three-dimensional Full Potential code FLO22 in 1975. Many Full Potential codes emerged after this, culminating in Boeing's Tranair (A633) code, which still sees heavy use. Transonic is an aeronautics term referring to a range of velocities just below and above the speed of sound. ... 1970 (MCMLXX) was a common year starting on Thursday. ... New York University (NYU) is a major research university in New York City. ... The Grumman Aircraft Engineering Corporation, later Grumman Aerospace Corporation, was a leading producer of military and civilian aircraft of the 20th century. ... Antony Jameson (1934, Gillingham, Kent UK) is an aeronautical engineer known for his pioneering work in the field of Computational Fluid Dynamics. ... 1975 (MCMLXXV) was a common year starting on Wednesday. ...

The next step was the Euler equations, which promised to provide more accurate solutions of transonic flows. The methodology used by Jameson in his three-dimensional FLO57 code (1981) was used by others to produce such programs as Lockheed's TEAM program and IAI/Analytical Methods' MGAERO program. MGAERO is unique in being a structured cartesian mesh code, while most other such codes use structured body-fitted grids (with the exception of NASA's TIGER/CART3D code, Lockheed's SPLITFLOW code and Georgia Tech's NASCART-GT, which is in fact a Navier-Stokes solver). Antony Jameson also developed the three-dimensional AIRPLANE code (1985) which made use of unstructured tetrahedral grids. 1981 (MCMLXXXI) was a common year starting on Thursday of the Gregorian calendar. ... Cartesian means of or relating to the French philosopher and mathematician René Descartes. ... Georgia Institute of Technology The Georgia Institute of Technology, or Georgia Tech, is located in Atlanta, Georgia, U.S.A. With over 16,000 students, Georgia Tech is one of four public research universities in the University System of Georgia. ... Antony Jameson (1934, Gillingham, Kent UK) is an aeronautical engineer known for his pioneering work in the field of Computational Fluid Dynamics. ... 1985 (MCMLXXXV) was a common year starting on Tuesday of the Gregorian calendar. ...

In the two-dimensional realm, Mark Drela and Michael Giles, then graduate students at MIT, developed the ISES Euler program (actually a suite of programs) for airfoil design and analysis. This code first became available in 1986 and has been further developed to design, analyze and optimize single or multi-element airfoils, as the MSES program. MSES sees wide use throughout the world. A derivative of MSES, for the design and analysis of airfoils in a cascade, is MISES, developed by Harold "Guppy" Youngren while he was a graduate student at MIT. 1986 (MCMLXXXVI) was a common year starting on Wednesday of the Gregorian calendar. ... Binomial name Poecilia reticulata Peters, 1859 Guppy standards The guppy (), also commonly known as guppie, is one of the most popular freshwater aquarium fish species in the world. ...

The Navier-Stokes equations were the ultimate target of developers. Two-dimensional codes, such as NASA Ames' ARC2D code first emerged. A number of three-dimensional codes were developed, leading to numerous commercial packages.

Technicalities

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 viscous 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 schems such as Total Variation Diminishing, Flux Corrected Transport, Essentially NonOscillatory, or MUSCL schemes are needed to avoid spurious oscillations in the solution. Lastly, if the problem is highly dynamic and occupies a wide range of scales, tcally modified in time, as in adaptive mesh refinement methods. Example of unstructured grid for a finite element analysis mesh. ... Example of regular grid. ... In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will terminate in a defined end-state. ... In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ... Typical high-resolution scheme based on MUSCL reconstruction. ... In systems described by partial differential equations, such as the following hyperbolic advection equation, the total variation (TV) is given by, and the total variation for the discrete case is, A numerical method is said to be total variation diminishing (TVD) if, For physically realisable systems where there is energy... In numerical analysis, central to any Eulerian method is the manner in which it discretizes the continuous domain of interest into a grid of many individual elements. ...

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 Reynolds-averaged Navier-Stokes equations (RANS) formulation, with the k-ε model or the Reynolds stress model, are two techniques for dealing with these scales. Smoothed Particle Hydrodynamics (SPH) is a computational method used for simulating fluid flows. ... In applied mathematics, Spectral methods are algorithms to solve certain kinds of partial differential equations numerically using some sort of Fast Fourier Transform. ... In mathematics, the spherical harmonics are the angular portion of an orthogonal set of solutions to Laplaces equation represented in a system of spherical coordinates. ... In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivres formula and which are easily defined recursively, like Fibonacci or Lucas numbers. ... Lattice Boltzmann methods or LBM are CFD methods for fluid simulation. ... In physics and chemistry, the mesoscopic scale refers to the length scale at which one can reasonably discuss the properties of a material or phenomenon without having to discuss the behavior of individual atoms. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ... Laminar flow (bottom) and turbulent flow (top) over a submarine hull. ... A direct numerical simulation (DNS) is a simulation in computational fluid dynamics in which the Navier-Stokes equations are numerically solved without any turbulence model. ... Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain faster results. ... Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow. ... The Reynolds-averaged Navier-Stokes equations are time-averaged equations of motion for fluid flow. ...

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). The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ... In chemistry, concentration is the measure of how much of a given substance there is mixed with another substance. ... Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ... In thermal physics, heat transfer is the passage of thermal energy from a hot to a cold body. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... Human blood smear: a - erythrocytes; b - neutrophil; c - eosinophil; d - lymphocyte. ...

Methodology

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

• During preprocessing
  • The geometry (physical bounds) of the problem is defined.
  • The volume occupied by the fluid is divided into discrete cells (the mesh). The mesh may be uniform or non uniform.
  • The physical modeling 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 simulation is started and the equations are solved iteratively as a steady-state or transient.
• Finally a postprocessor is used for the analysis and visualization of the resulting solution.

In Computer aided engineering (CAE) a preprocessor is a program which provides a Graphical user interface (GUI) to define physical properties. ... Table of Geometry, from the 1728 Cyclopaedia. ... The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. ...

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. In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ...

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):

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 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. The FEM formulation has been adapted for use with the Navier-Stokes equations. In this method, a weighted residual equation is formed:

where R_i is the equation residual at an element vertex i , Q is the conservation equation expressed on an element basis, W_i is the weight factor and V^e is the volume of the element.

• 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.

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 necessitates the application of flux limiters to ensure that the solution is total variation diminishing.

The finite volume method is a method for representing and evaluating partial differential equations as algebraic equations. ... In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ... Mathematically, the finite element method (FEM) is used for finding approximate solution of partial differential equations (PDE) as well as of integral equations such as the heat transport equation. ... A finite difference is a mathematical expression of the form f(x + b) − f(x +a). ... The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i. ... Typical high-resolution scheme based on MUSCL reconstruction. ... Flux limiters are used in high resolution schemes — numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations. ... In systems described by partial differential equations, such as the following hyperbolic advection equation, the total variation (TV) is given by, and the total variation for the discrete case is, A numerical method is said to be total variation diminishing (TVD) if, For physically realisable systems where there is energy...

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. A direct numerical simulation (DNS) is a simulation in computational fluid dynamics in which the Navier-Stokes equations are numerically solved without any turbulence model. ...

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 stresses. 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. The Reynolds-averaged Navier-Stokes equations are time-averaged equations of motion for fluid flow. ... In fluid dynamics, the Reynolds stresses (or, the Reynolds stress tensor) is the stress tensor in a fluid due to the random turbulent fluctuations in fluid momentum. ...

RANS models can be divided into two broad approaches:

1. Boussinesq hypothesis: This method involves using an algebraic equation for the Reynolds stresses which include determining the turbulent viscosity, and depending on the level of sophistication of the model, solving transport equations for determining the turbulent kinetic energy and dissipation. Models include k-ε (Spalding), Mixing Length Model (Prandtl) and Zero Equation (Chen). The models available in this approach are often referred to by the number of transport equations they include, for example the Mixing Length model is a "Zero Equation" model because no transport equations are solved, and the k-ε on the other hand is a "Two Equation" model because two transport equations are solved.
2. Reynolds stress model (RSM): This approach attempts to actually solve transport equations for the Reynolds stresses. This means introduction of several transport equations for all the Reynolds stresses and hence this approach is much more costly in CPU effort.

In fluid dynamics, the Boussinesq approximation is used in the field of buoyancy-driven flow. ...

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. Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow. ...

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-Allmaras 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. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

Vortex method

The Vortex method is a grid-free technique for the simulation of turbulent flows. It uses vortices as the computational elements, mimicking the physical structures in turbulence. Vortex methods were developed as a grid-free methodology that would not be limited by the fundamental smoothing effects associated with grid-based methods. To be practical, however, vortex methods require means for rapidly computing velocities from the vortex elements – in other words they require the solution to a particular form of the N-body problem (in which the motion of N objects is tied to their mutual influences). A long-sought breakthrough came in the late 1980’s with the development of the Fast Multipole Method (FMM), an algorithm that has been heralded as one of the top ten advances in numerical science of the 20th century. This breakthrough paved the way to practical computation of the velocities from the vortex elements and is the basis of successful algorithms.

Software based on the Vortex method offer the engineer a new means for solving tough fluid dynamics problems with minimal user intervention. All that is required is specification of problem geometry and setting of boundary and initial conditions. Among the significant advantages of this modern technology;

• It is practically grid-free, thus eliminating numerous iterations associated with RANS and LES.
• All problems are treated identically. No modeling or calibration inputs are required.
• Time-series simulations, which are crucial for correct analysis of acoustics, are possible.
• The small scale and large scale are accurately simulated at the same time.

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 cannot 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. The Gauss-Seidel method is a technique used to solve a linear system of equations. ... Successive over-relaxation (SOR) is a numerical method used to speed up convergence of the Gauss-Seidel method for solving a linear system of equations. ... This article needs to be cleaned up to conform to a higher standard of quality. ... In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive definite. ... It has been suggested that this article or section be merged with Multigrid method. ...

Motivation

The techniques are widely used by engineers designing or analysing devices that interact with fluid, such as vehicles, pumps, chemical apparatus or ventilation systems. Engineering is the application of scientific and technical knowledge to solve human problems. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...

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+ and CFD-FASTRAN by ESI GROUP, CFdesign by Blue Ridge Numerics, CFX by ANSYS Inc., Coolit, COSMOSFloWorks by SolidWorks, EFD.Lab; EFD.Pro; EFD;V5 by NIKA GmbH & Flomerics, FLOW-3D(R) by Flow Science, Inc, FLUENT, KIVA, NUMECA, Phoenics, STAR-CD by CD-adapco, CFDExpert by Zeus Numerix. Other software packages serve as add-ons or complementary products to CFD tools. These include EnSight or FIELDVIEW or Tecplot for post-processing and KINetics for solving detailed chemical kinetics. CFD-ACE+ is a general, Computational Fluid Dynamics (CFD) and multiphysics solver for a broad range of physics disciplines. ... CFD-FASTRAN is the leading commercial Computational Fluid Dynamics(CFD) software for aerodynamic and aerothermodynamic applications. ... ESI Group’s CFD Operations based in Huntsville, Alabama develops and markets software for Computational Fluid Dynamics(CFD). ... CFX is a commercial computational fluid dynamics (CFD) program widely employed within industry. ... ANSYS Inc. ... The Coolit thermal design software, from Daat Research Corp. ... Fluent can refer to: the software produced by Fluent, Inc. ... Zeus Numerix Private Limited is a company dedicated to providing high class products and customized solutions in the field of Computational Fluid Dynamics. ... This page may meet Wikipedia’s criteria for speedy deletion. ... Tecplot refers to a Computational Fluid Dynamics (CFD) and numerical simulation software package used in post-processing simulation results. ...

The major problem faced by the CFD industry today is a shortage of skilled human resource. CFD development requires a 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.

More recently, there has been a shift away from the numerical expert usage of CFD tools. This shift takes advantage of the engineer’s knowledge of the physical phenomena and employs intelligent solution controls to handle numerical nuances automatically based on common engineering input data.

See also

• Visualization
• Blade element theory
• Finite element analysis
• Wind tunnel
• Fluid mechanics

Visualization of how a car deforms in an asymmetrical crash using finite element analysis. ... Blade element theory is a mathematical process originally designed in the nineteenth century to determine the behaviour of propellors. ... Visualization of how a car deforms in an asymmetrical crash using finite element analysis. ... NASA wind tunnel with the model of a plane A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects. ... Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ...

External links

• CFD-Wiki
• CFD Online
• CFD Review
• High Performance Computing and Clustering Portal for Linux and Windows.
• Course: Introduction to CFD -- Dmitri Kuzmin (University of Dortmund)