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• Governing equations
  *[[Navier-Stokes equations]] *[[Favre averaged Navier-Stokes equations]]
  72 B (6 words) - 04:55, 4 October 2005
• Favre averaged Navier-Stokes equations
  == Instantaneous equations == To close these equations it is also necessary to specify an equation of state. Assuming a caloricall
  15 KB (2,374 words) - 20:33, 24 November 2005
• Navier-Stokes equations
  ...Usually, the term Navier-Stokes equations is used to refer to all of these equations. ==Equations==
  29 KB (4,606 words) - 18:17, 28 August 2012
• Favre Averaged Navier-Stokes Equations
  #redirect [[Favre averaged Navier-Stokes equations]]
  52 B (5 words) - 10:29, 7 September 2005
• Governing Equations
  #redirect [[Governing equations]]
  33 B (3 words) - 12:21, 7 September 2005
• Reynolds averaged equations
  ==The Reynolds averaged equations and the turbulence closure problem== === The equations governing the instantaneous fluid motions ===
  17 KB (2,883 words) - 22:16, 14 May 2006
• Solution of Navier-Stokes equations
  ...traditional CFD algorithms require the solution of the Navier-Stokes (N-S) equations. There are two important issues that arise in the solution process: # The N-S equations are nonlinear.
  2 KB (330 words) - 10:01, 23 April 2009
• Introduction to turbulence/Reynolds averaged equations
  == Equations governing instantaneous fluid motion == All fluid motions, whether turbulent or not, are governed by the dynamical equations for a fluid. These can be written using Cartesian tensor notation as:
  45 KB (7,578 words) - 08:35, 21 August 2013
• Reynolds averaged equations and the Turbulence Closure Problem
  #REDIRECT [[Reynolds averaged equations and the turbulence closure problem]]
  76 B (9 words) - 17:00, 1 April 2007
• Reynolds averaged equations and the turbulence closure problem
  #REDIRECT [[Introduction to turbulence/Reynolds averaged equations]]
  68 B (7 words) - 10:04, 17 December 2008
• Solve UV.f90 - Solution of the momentum equations for U and V
  6 KB (932 words) - 14:58, 19 May 2016
• TDMA.f90 - Solution of system of linear equations by Thomas method
  ! solution of linear system of equations by Thomas algorithm modul
  2 KB (341 words) - 15:00, 19 May 2016

Page text matches

• Reference section
  The goal is to provide comprehensive coverage of fluid dynamics, governing equations, turbulence modeling, numerics, discretization schemes, solvers, heat trans
  410 B (43 words) - 07:06, 3 September 2013
• Codes
  ...y for Finite Element Method. Requires knowledge of weak forms of governing equations || Various types - Gmsh, Abaqus, Metis, Diffpack etc ...allel, finite-volume based Navier–Stokes and convection–diffusion like equations solver -- [https://flubiopetsc.github.io/flubiopetsc/ FLUBIO homepage]|| un
  25 KB (3,558 words) - 08:31, 23 January 2024
• Fluid dynamics
  ...tion of a viscous, heat conducting fluid. Various simplifications of these equations exist depending on which effects are insignificant. There are several dimen *[[Governing equations | Governing Equations]]
  2 KB (205 words) - 10:17, 13 March 2013
• Isentropic flow relations
  [[category: Equations]]
  3 KB (519 words) - 18:04, 19 December 2008
• Governing equations
  *[[Navier-Stokes equations]] *[[Favre averaged Navier-Stokes equations]]
  72 B (6 words) - 04:55, 4 October 2005
• Favre averaged Navier-Stokes equations
  == Instantaneous equations == To close these equations it is also necessary to specify an equation of state. Assuming a caloricall
  15 KB (2,374 words) - 20:33, 24 November 2005
• Reynolds number
  ...ds]] in his famous [[pipe flow experiments]]. Consider the [[Navier-Stokes equations|momentum equation]] which is given below
  3 KB (450 words) - 09:15, 3 January 2012
• Osborne Reynolds
  ...of turbulent flow, for example using the [[Reynolds averaged Navier-Stokes equations]].
  1 KB (219 words) - 14:15, 13 September 2005
• Navier-Stokes equations
  ...Usually, the term Navier-Stokes equations is used to refer to all of these equations. ==Equations==
  29 KB (4,606 words) - 18:17, 28 August 2012
• Gerris Flow Solver
  ...pen source finite volume code for the solution of the partial differential equations describing fluid flow.
  425 B (61 words) - 13:17, 14 February 2008
• Vistur.f
  b) to define '''vist''' from user defined equations
  289 B (47 words) - 23:06, 6 September 2005
• Introduction to turbulence
  == [[Introduction to turbulence/Reynolds averaged equations|Reynolds averaged equations and the turbulence closure problem]] == ...Reynolds averaged equations#Equations governing instantaneous fluid motion|Equations governing instantaneous fluid motion]]
  8 KB (948 words) - 12:34, 15 March 2012
• Introduction to turbulence/Statistical analysis
  ... point or time how it will behave at another (at least without solving the equations). Moreover, a slight change in the intial or boundary conditions may cause ... of this chapter will be all we need to begin a discussion of the averaged equations of motion in <font color="orange">page ???</font>
  4 KB (544 words) - 18:06, 25 June 2007
• Reynolds stress model (RSM)
  == Equations == ...esses, <math>\rho\overline{u'_iu'_j}</math> , using differential transport equations. The individual Reynolds stresses are then used to obtain closure of the Re
  8 KB (1,203 words) - 01:47, 18 April 2017
• Near-wall treatment for k-omega models
  ...enter takes advantage of the fact that the solution to <math>\omega</math> equations is known for both viscous and log layer
  4 KB (581 words) - 10:40, 31 March 2021
• Favre Averaged Navier-Stokes Equations
  #redirect [[Favre averaged Navier-Stokes equations]]
  52 B (5 words) - 10:29, 7 September 2005
• Favre averaging
  Favre averaging can be used to derive the [[Favre averaged Navier-Stokes equations]].
  1 KB (209 words) - 21:48, 26 August 2013
• Governing Equations
  #redirect [[Governing equations]]
  33 B (3 words) - 12:21, 7 September 2005
• Direct numerical simulation (DNS)
  ... a simulation in computational fluid dynamics in which the [[Navier-Stokes equations]] are numerically solved without any [[turbulence]] model. This means that ...LES) and models for methods that solve the Reynolds-averaged Navier-Stokes equations (RANS). This is done by means of "a priori" tests, in which the input data
  4 KB (672 words) - 13:52, 25 July 2012
• Fluent FAQ
  ...for mass, momentum and energy) simultaneously instead of sequentially (the equations are segregated from one another). You should use the coupled solver when th
  39 KB (6,386 words) - 16:48, 26 April 2013
• Best practice guidelines for turbomachinery CFD
  ...tions, or require user coding to implement the correct source terms in the equations. Please contact your software distributor if your code does not have the qu ... Turbomachinery Flows – Part II – Rotor/Stator Interaction using Euler Equations|rest=AGARD Report CP-571}}
  41 KB (6,252 words) - 08:46, 4 March 2023
• Page name test
  ...ent, 1999) of turbulence. Thus, the RANS consists of partial differential equations that provide local information to the model, as well as accuracy, and a rat ...ion is a set of additional equations which, when solved with the mean-flow equations (RANS), permits the computation of the appropriate correlations (fluctuatin
  2 KB (352 words) - 21:51, 18 May 2006
• Baldwin-Lomax model
  == Equations == ...omax model the turbulence energy, <math>k</math>, present in the governing equations, is set to zero.
  8 KB (1,262 words) - 09:15, 3 January 2012
• Two equation turbulence models
  By definition, two equation models include two extra transport equations to represent the turbulent properties of the flow. This allows a two equati ...sistency with the turbulent boundary layer behaviour. This often makes the equations stiff and further increases computation time.
  11 KB (1,667 words) - 20:52, 25 October 2016
• Reynolds averaged equations
  ==The Reynolds averaged equations and the turbulence closure problem== === The equations governing the instantaneous fluid motions ===
  17 KB (2,883 words) - 22:16, 14 May 2006
• Introduction to turbulence/Nature of turbulence
  ...ith the equations used to describe the mechanics of turbulence. It is only equations which can give us the hope of predicting turbulence. But your study of this ...randomness, or just the solutions. And if the latter, was it something the equations did to them, or a consequence of the initial conditions?
  16 KB (2,597 words) - 21:12, 9 November 2016
• Ansys FAQ
  ...t to outlet. As a result, before judging the residual convergence of these equations, make sure their imbalances are close to zero. Most standard engineering equations we are familiar with use some "bulk temperature" in place of the Wall Adjac
  27 KB (4,461 words) - 02:03, 18 August 2018
• Numerical methods
  ## [[Classification of govering equations]] ### [[Integral form of govering equations]]
  4 KB (399 words) - 12:42, 26 August 2012
• Fluid
  ... described by a set of partial differential equations, the [[Navier-Stokes equations]].
  1 KB (215 words) - 23:53, 13 September 2005
• Incompressible flow
  == Governing Equations == The [[Navier-Stokes equations]] for incompressible flow are
  8 KB (1,427 words) - 18:57, 19 August 2013
• Laplacian
  ...e effects (except in the case of [[wave equation]]). Some of the important equations are Solutions of these equations are very smooth and in most cases are infinitely differentiable (when the a
  3 KB (414 words) - 08:19, 12 April 2007
• Potential flow
  == Governing equations ==
  800 B (127 words) - 13:06, 16 March 2016
• Inviscid flow
  ==Governing Equations== ...s'', are obtained by discarding the viscous terms from the [[Navier-Stokes equations]]
  2 KB (323 words) - 07:46, 20 August 2013
• Stream function
  Comparing the two equations, we have
  1 KB (192 words) - 11:39, 12 September 2005
• Introduction to CFD
  ...Numerical methods | numerically]]. The complex set of partial differential equations are solved on in geometrical domain divided into small volumes, commonly kn
  2 KB (401 words) - 06:50, 8 January 2013
• Adams methods
  ...merical integration]] of initial value problems in [[Ordinary Differential Equations]] (ODE's). [[Multi-step methods]] benefit from the fact that the computatio
  1,023 B (171 words) - 18:53, 13 August 2007
• Lid-driven cavity problem
  ...82|title=High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method|rest=Journal of Computational Physics, Vol. 48, pp.
  3 KB (546 words) - 12:44, 9 April 2013
• Introduction to numerical methods
  ...ons. In turbulence modeling for example, one is interested in devising new equations for the extra unknowns that resulted from the averaging process.
  1 KB (222 words) - 21:02, 24 May 2007
• Large eddy simulation (LES)
  ...ressible flows. For compressible flows, see [[Favre averaged Navier-Stokes equations]]. The filtered equations are developed from the incompressible [[Navier-Stokes equations]] of motion:
  6 KB (882 words) - 21:50, 24 June 2013
• Finite volume
  ...lume. The next step is to integrate the differential form of the governing equations (very similar to the control volume approach) over each control volume. Int FVM is also preferred while solving partial differential equations containing discontinuous coefficients.
  4 KB (643 words) - 09:15, 3 January 2012
• RNG k-epsilon model
  ...) methods by [[#References|Yakhot et al]] to renormalise the Navier-Stokes equations, to account for the effects of smaller scales of motion. In the standard k- == Transport Equations==
  3 KB (480 words) - 02:44, 5 June 2010
• Standard k-epsilon model
  == Transport equations for standard k-epsilon model ==
  3 KB (401 words) - 20:15, 16 December 2014
• Approximation Schemes for convective term
  ...ed the discretization schemes of the convective terms in the finite-volume equations. The accuracy, numerical stability and the boundness of the solution depend == Basic Equations of CFD ==
  30 KB (4,389 words) - 06:47, 16 September 2005
• Approximation Schemes
  ...ed the discretization schemes of the convective terms in the finite-volume equations. The accuracy, numerical stability and the boundness of the solution depend == Basic Equations of CFD ==
  16 KB (2,286 words) - 18:01, 14 September 2005
• Gauss-Seidel method
  The '''Gauss-Seidel method''' is a technique used to solve a linear system of equations. The method is named after the German mathematician [http://en.wikipedia.or We seek the solution to a set of linear equations: <br>
  8 KB (1,113 words) - 09:15, 3 January 2012
• Jacobi method
  ...ithm in linear algebra for determining the solutions of a system of linear equations with largest absolute values in each row and column dominated by the diagon We seek the solution to set of linear equations: <br>
  6 KB (825 words) - 09:15, 3 January 2012
• Successive over-relaxation method - SOR
  We seek the solution to set of linear equations <br>
  2 KB (364 words) - 02:08, 19 December 2005
• Iterative methods
  We seek the solution to the linear system of equations <br>
  2 KB (262 words) - 14:17, 19 December 2008
• 2-D vortex in isentropic flow
  This is one of the few exact solutions for the compressible Euler equations. The test case involves [[convection]] of an [[isentropic]] [[vortex]] in [
  2 KB (242 words) - 04:00, 21 October 2014
• Viscous diffusion of multiple vortex system
  continuity and momentum equations in dimension-less form in the domain <math>0
  575 B (107 words) - 07:40, 12 April 2007
• Ringleb flow
  Streamline equations:
  827 B (120 words) - 08:32, 16 September 2005
• Conjugate gradient methods
  For the system of equations: <br>
  1 KB (170 words) - 17:49, 26 August 2006
• Fixed point theorem
  ==Application to solution of linear system of equations==
  6 KB (1,062 words) - 15:25, 4 December 2006
• Stone's method
  ...al differential equations. This method does not apply to generic system of equations. ...lution of Implicit Approximations of Multidimensional Partial Differential Equations|rest=SIAM Journal of Numerical Analysis, 1968, vol. 5, pp. 530–538}}
  3 KB (380 words) - 09:42, 12 May 2007
• Combustion
  == Transport Equations == ...ansport equations for a reacting flow are the energy and species transport equations with their appropriate boundary conditions that may be of Dirichlet or Neum
  156 KB (25,897 words) - 22:14, 17 March 2011
• Realisable k-epsilon model
  == Transport Equations == In these equations, <math> P_k </math> represents the generation of turbulence kinetic energy
  2 KB (380 words) - 19:57, 16 December 2014
• Detached eddy simulation (DES)
  ...enter's SST model uses a turbulence length scale obtained from the model's equations and compares it with the grid length scale to switch between LES and RANS [
  3 KB (456 words) - 09:56, 17 December 2008
• Dynamic subgrid-scale model
  Filtering with the grid filter results in the normal LES equations, with <math>\tau_{ij}</math> given by Filtering again with the test filter results in a similar set of equations, but
  3 KB (505 words) - 19:56, 8 May 2007
• Approximation Schemes for convective term - structured grids - Common
  ... describes the discretization schemes of convective terms in finite-volume equations. The accuracy, numerical stability, and boundedness of the solution depend == Basic Equations of CFD ==
  28 KB (4,096 words) - 13:11, 24 October 2016
• Scramjet intake
  ...is of the scramjet-inlet flow field by using two-dimensional Navier-Stokes equations | rest=Technical Paper 1940, NASA}}
  433 B (49 words) - 08:19, 19 September 2005
• Mesh generation
  ...of three methods is used to solve the approximate version of the system of equations: finite volumes, finite elements, or finite differences. Care must taken t
  11 KB (1,840 words) - 10:16, 21 August 2006
• Gaussian elimination
  We consider the system of linear equations '''<math> A\phi = b </math>''' or <br> To perform Gaussian elimination starting with the above given system of equations we compose the '''augmented matrix equation''' in the form: <br>
  4 KB (525 words) - 15:08, 22 August 2007
• LU decomposition
  Consider the system of equations <math>A\vec{x}=\vec{b}</math>, where <math>A</math> is an <math>n\times n</ ... probably best used for relatively small, relatively non-sparse systems of equations (with small and non-sparse open to some interpretation). For larger and/or
  4 KB (696 words) - 09:22, 21 November 2011
• Tridiagonal matrix algorithm - TDMA (Thomas algorithm)
  ... Gaussian elimination that can be used to solve ''tridiagonal'' systems of equations. A tridiagonal system may be written as In other situations, the system of equations may be ''block tridiagonal'', with smaller submatrices arranged as the indi
  4 KB (658 words) - 22:58, 14 September 2016
• Velocity-pressure coupling
  ...consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter- ...gated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matri
  2 KB (377 words) - 05:50, 24 October 2005
• Stokes flow
  ==Governing equations==
  494 B (72 words) - 08:30, 20 August 2013
• Schemes by Leonard - structured grids
  equations. Technical Memorandum TM-100916 ICOMP-88-11, NASA, 1988.
  4 KB (518 words) - 20:23, 1 July 2008
• Meshing
  ...of three methods is used to solve the approximate version of the system of equations: finite volumes, finite elements, or finite differences. Care must be take
  2 KB (313 words) - 09:15, 3 January 2012
• Algebraic multigrid - AMG
  ...eferred to as an '''algebraic multigrid''' scheme because the coarse level equations are generated without the use of any geometry or re-discretization on the c
  2 KB (299 words) - 08:14, 18 September 2006
• Geometric multigrid - FAS
  In Geometric multigrid a hierarchy of meshes is generated.The discretized equations are evaluated on every level. The advantage of geometric multigrid over alg
  2 KB (297 words) - 09:19, 6 February 2012
• SIMPLE algorithm
  ==SIMPLE [Semi-Implicit Method for Pressure-Linked Equations]==
  3 KB (442 words) - 10:42, 11 March 2016
• Solution of Navier-Stokes equations
  ...traditional CFD algorithms require the solution of the Navier-Stokes (N-S) equations. There are two important issues that arise in the solution process: # The N-S equations are nonlinear.
  2 KB (330 words) - 10:01, 23 April 2009
• Sand box Approximation Schemes
  ... resolution scheme]]s for the numerical solution of [[partial differential equations]]. :''Linear numerical schemes for solving [[partial differential equations]] (PDE's), having the property of not generating new extrema ([[monotone sc
  26 KB (3,687 words) - 20:19, 7 November 2011
• Aero-acoustics and noise
  ...ted an &quot;Acoustic Analogy&quot;. With proper manipulation of the Euler equations, he derived a wave equation based on pressure as the fluctuating variable, ...ations, while the acoustic field is obtained by the perturbed compressible equations (PCE). This splitting method has further been modified by Shen and Sorenson
  5 KB (709 words) - 15:59, 23 June 2013
• Time discretisation
  With regard to the semi-discretised Navier-Stokes equations (NSE), there are two distinct cases to consider. These are the cases where the resulting system of equations are
  7 KB (1,005 words) - 02:25, 20 January 2008
• Linear Schemes - structured grids
  ...1966 | title= Application of oscillation matrices to diffusion-convection equations | rest= Journal Math. and Phys., Vol. 45, p.301, (1966) }}
  4 KB (543 words) - 01:11, 9 November 2005
• NSC2KE
  ...ic flows on unstructured triangular meshes. To solve the Euler part of the equations, a Roe, an Osher and a Kinetic solvers are available. To compute turbulent
  873 B (151 words) - 03:54, 21 October 2005
• Runge Kutta methods
  ...ions and Continuity Equations result in a system of Differential Algebraic Equations (DAE), ''not'' in [[ODE]]. Dealing a DAE is different than dealing an [[ODE
  2 KB (388 words) - 01:44, 26 May 2007
• Explosion test in 2-D
  The two dimensional Euler equations are solved on a square domain 2x2 in the xy-plane. The initial conditions c ...has circular symmetry, the 2-D Euler equations can be reduced to 1-D Euler equations in the radial coordinate r,
  2 KB (312 words) - 06:16, 2 November 2005
• Machine precision
  ...nts can be very small which requires using double precision. The choice of equations can also be important and can be made intelligently. For example, if you wa
  3 KB (485 words) - 04:14, 29 November 2005
• OpenFlower
  ...ly devoted to the resolution of the turbulent incompressible Navier-Stokes equations, with scalar transport. It can deal with arbitrary complex geometries with
  3 KB (388 words) - 20:06, 7 June 2007
• Algebraic turbulence models
  ...lence models are models that do not require the solution of any additional equations, and are calculated directly from the flow variables. As a consequence, zer
  1 KB (165 words) - 20:39, 1 April 2007
• Mesh adaptation
  ...nique is to treat the mesh as if it is an elastic solid and solve a system equations (suject to some forcing) that deforms the original mesh (see for instance [
  8 KB (1,236 words) - 09:43, 17 May 2012
• V2-f models
  ...tion of <math>\zeta</math>, the new transport equation is derived from the equations for <math>\overline{\upsilon^2}</math> and <math>k</math>, and solved inste ==The <math>\overline{\upsilon^2} - f</math> equations==
  6 KB (917 words) - 05:45, 7 February 2014
• Cebeci-Smith model
  == Equations == ...ci, T. |year=1967|title=Numerical solution of the turbulent boundary layer equations|rest=Douglas aircraft division report DAC 33735}}
  3 KB (419 words) - 12:13, 18 December 2008
• Johnson-King model
  ...ferential Equation (PDE) (Normally for popular turbulence models transport equations are solved which are PDE's). This model solves for a transport equation for
  735 B (103 words) - 05:48, 17 January 2012
• General CFD FAQ
  ... every volume the governing equations are solved. The resulting system of equations usually involves fluxes of the conserved variable, and thus the calculation ...oundary conditions may be more difficult to formulate. Again, a system of equations is obtained (usually for nodal values) that must be solved to obtain a solu
  7 KB (1,199 words) - 13:47, 5 June 2013
• CHAM FAQ
  ... partial differential equations are converted into algebraic finite-volume equations with the aid of discretisation assumptions for the transient, convection, d For curvilinear coordinates, the default option is to solve the momentum equations in terms of the covariant projections of the velocity vector into the local
  37 KB (5,717 words) - 12:46, 9 December 2019
• Continuum
  ...nd time and may apply differential equations in the analysis of processes. Equations derived on the basis of this assumption have withstood the test of time and
  1 KB (180 words) - 21:40, 22 November 2005
• Flux limiters
  ...s and discontinuity that arises in hyperbolic equations. Physically, these equations model the convective fluid flow. It has been observed that low-order scheme
  2 KB (361 words) - 10:19, 22 February 2007
• Introduction and need
  ...kes equations (and most other physical phenomena) yield a linear system of equations that needs to be solved. The need for robust, efficient, and relatively fas ...ummary of most iterative methods used in the solution of linear systems of equations. It also includes a pseudocode for each method.
  2 KB (267 words) - 22:11, 13 December 2005
• Finite difference
  ..., which aim at the numerical solution of ordinary and partial differential equations respectively. The resulting methods are called ''finite-difference methods' The [[Numerical ordinary differential equations#The Euler method|Euler method]] for solving this equation uses the finite d
  7 KB (1,123 words) - 16:29, 13 May 2008
• Finite element
  ...ations as there are unknowns (the a's) thus yielding a albegraic system of equations.
  1 KB (226 words) - 12:09, 31 August 2011
• Kato-Launder modification
  ==Basic equations==
  6 KB (938 words) - 09:12, 12 June 2007
• Discretization of the transient term
  ...ution at each time step. The spatial discretization for the time-dependent equations is identical to the steady-state case. <br> ... discretization involves the integration of every term in the differential equations over the time step <math>\Delta t \,</math>. The integration of transient e
  6 KB (1,008 words) - 18:40, 19 July 2007
• Dimensional analysis
  Engineers often have to make experiments, because the governing equations of fluid flow are impossible to
  8 KB (1,433 words) - 16:55, 13 December 2005
• Dimensional analysis (introductory)
  Engineers often have to make experiments, because the governing equations of fluid flow are impossible to
  8 KB (1,439 words) - 04:47, 3 November 2008
• Generic scalar transport equation
  ...s are the basis for the derivation of differential or integro-differential equations. In this respect, any differential equation addresses a certain quantity as ...uations governing various physical phenomena will reveal that all of these equations can be put into a generic form thus allowing a systematic approach for a co
  4 KB (582 words) - 03:37, 14 February 2006
• Direct methods
  Direct methods for the solution of the linear system of equations ...f Gaussian elimination or are based upon a particular factorization of the equations that will allow an exact computation. [[LU decomposition]] is both a facto
  871 B (126 words) - 05:19, 24 May 2007
• GPGPU
  ...se the graphics card to compute, and then display the results of their CFD equations. OpenGL hooks into C++ to enable that, and Microsoft's DirectX performs a s ... Knut-Andreas Lie and Jostein R. Natvig |year=2006|title=Solving the Euler Equations on Graphics Processing Units|rest=in collection Proceedings of the 6th Inte
  8 KB (1,175 words) - 01:03, 22 March 2010