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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
• Two phase flow
  Resolution of these equations requires the knowledge of the instantaneous velocity of the fluid at partic
  13 KB (2,060 words) - 11:38, 6 December 2010
• Wall modeling
  ...ry poor in the Ke model hence the near wall region is approximated by wall equations. This is achieved by having the first cell in the turbulent region by calcu
  198 B (36 words) - 05:41, 2 March 2006
• Near-wall treatment for LES models
  ...be determined from an algebraic law-of-the-wall model or from differential equations solved on a near-wall-layer grid refined in ...d into the main flow,and the following simplified turbulent boundary-layer equations are solved:
  3 KB (497 words) - 12:30, 8 June 2006
• Boussinesq eddy viscosity assumption
  *[[Introduction to turbulence/Reynolds averaged equations#Turbulence closure problem and eddy viscosity|Turbulence closure problem an
  2 KB (292 words) - 09:15, 3 January 2012
• Skin friction coefficient
  ''Add proper reference for equations in [2]''
  4 KB (516 words) - 12:14, 14 January 2016
• Low-Re k-epsilon models
  ==Governing equations==
  6 KB (842 words) - 09:58, 17 December 2008
• Introduction to turbulence/Statistical analysis/Ensemble average
  .... Only ensemble averages will be used in the development of the turbulence equations here unless otherwise stated.
  8 KB (1,391 words) - 12:29, 2 July 2011
• 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
• FENSAP-ICE
  ...rom FENSAP, or other CFD codes, and solves fine-grain partial differential equations for droplet velocity and concentration everywhere in the field. While a few ...ule of the FENSAP-ICE system. ICE3D solves fine-grain partial differential equations for thermodynamics and yields the 3-D shape of ice and the water film thick
  2 KB (299 words) - 14:56, 15 December 2006
• Flow around a circular cylinder
  ....A., 1996, Steady-state numerical solution of the Navier-Stokes and energy equations around a horizontal cylinder at moderate Reynolds numbers from 100 to 500,
  6 KB (884 words) - 11:31, 8 April 2017
• Introduction to turbulence/Turbulence kinetic energy
  ... the Navier-Stokes equations as a starting point has left us with far more equations than unknowns. Unfortunately this means that the turbulence ... a simple solution: we simply cannot produce a set of reasonably universal equations. Obviously we are going to have to study the turbulence fluctuations in mor
  47 KB (7,664 words) - 12:47, 13 December 2013
• CFD-FASTRAN
  ...r Stokes equations of flow but the user can solve the reduced Euler set of equations by selecting the inviscid option. For turbulent flows, the software support
  2 KB (337 words) - 09:53, 17 December 2008
• Jeffery-Hamel flow
  The Navier-Stokes equations in cylindrical coordinates then reduce to
  5 KB (777 words) - 21:03, 1 September 2006
• Discontinuous Galerkin
  solve the Euler equations by Cockburn and Shu. The solution of the Navier-Stokes equations with the DG method was first accomplished by Bassi and Rebay in 1997.
  9 KB (1,518 words) - 09:15, 3 January 2012
• K-epsilon models
  ...n models|two equation model]], that means, it includes two extra transport equations to represent the turbulent properties of the flow. This allows a two equati
  3 KB (406 words) - 16:03, 18 June 2011
• K-omega models
  ...n models|two equation model]], that means, it includes two extra transport equations to represent the turbulent properties of the flow. This allows a two equati
  1 KB (148 words) - 12:43, 12 October 2011
• NOGRID
  ...and continuum mechanical problems. FPM is a method for the solution of the equations governing viscous fluid flows, including the effects of heat and mass trans
  3 KB (408 words) - 07:32, 14 June 2018
• Zeta-f model
  ... relaxation model. For the incompressible Newtonian fluid the final set of equations constituting the <math>\zeta-f</math> model is given below.
  3 KB (440 words) - 10:06, 17 December 2008
• J-FLO
  ...quations and whose solution cost is comparable to that of solving the flow equations. Thus, the gradient can be determined with roughly the computational costs ...ude analysis and optimal control capabilities using Euler or Navier-Stokes equations, with automatically generated structured or unstructured body-conforming gr
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• 2-D laminar/turbulent driven square cavity flow
  ...ng area" for approbation of [[approximation schemes]] for terms in initial equations as well as of [[computational models]] and methods. A large number of calcu ....{{fact} In the earliest renditions of this problem, the [[Navier–Stokes equations]] were transformed into [[vorticity–stream function]] variables for econo
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• PHOENICS
  ... 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
  11 KB (1,641 words) - 11:18, 5 July 2013
• Transition to turbulence
  ...minar flow and turbulence flows are special solutions of the navier stokes equations. The latter predominates in flows with vanishing viscosity. The Reynolds nu
  4 KB (558 words) - 00:11, 23 May 2007
• Cfd simulation of vortex shedding
  ...ions in time. In [[Compressible flow|compressible fluids]], the governing equations are often written in terms of the [[conservative form]] of [[Euler's equati ...he top, bottom, and right boundaries. The quantities of the Navier-Stokes equations were non-dimensionalized and the [[Schemes_by_Leonard_-_structured_grids|QU
  4 KB (584 words) - 23:32, 29 October 2008
• Discrete Poisson equation
  [[Category:Numerical differential equations]]
  8 KB (1,117 words) - 16:32, 25 May 2007
• NaSt2D-2.0
  ...e SOR-method ('''''successive over-relaxation''''') the '''''Navier-Stokes equations''''', discreted by finite difference method, in a staggered rectangle grid
  912 B (120 words) - 09:35, 11 October 2016
• SSIIM
  ...Simulation in Intakes with Multiblock Option. It solves the Navier-Stokes equations using the control volume method with the SIMPLE algorithm and the k-epsilon
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• A roughness-dependent model
  Figure (1) shows that the velocity profile obtained from equations (8), (4) and (5) (solid line) is more accurate than the logarithmic velocit
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• Reynolds averaged equations and the turbulence closure problem
  #REDIRECT [[Introduction to turbulence/Reynolds averaged equations]]
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• Tdyn
  ...is also possible to configure additional user defined partial differential equations (PDE) solvers and couple the new variables with any of the other problems.
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• FDS
  ... applications. The software solves numerically a form of the Navier-Stokes equations appropriate for low-speed, thermally-driven flow with an emphasis on smoke
  797 B (125 words) - 14:36, 28 August 2007
• Introduction to turbulence/Stationarity and homogeneity
  Homogeneity will be seen to have powerful consequences for the equations govering the averaged motion, since the spatial derivative of any averaged
  41 KB (6,536 words) - 09:19, 25 February 2008
• Non-equilibrium Flow
  ...then relaxation equations may be added to the conservation (Navier{Stokes) equations. In the other extreme case of Knc > 1, as a pragmatic engineering approach, ...troduce these results in form of transition probabilities into the kinetic equations. Since, with increasing complexity of molecules, also the dimensionality in
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• Discrete Operator Splitting
  vectors for the momentum and the continuity equations,
  4 KB (587 words) - 16:25, 28 December 2010
• Introduction to turbulence/Free turbulent shear flows
  ...ever be possible to neglect the turbulent transport terms in the dynamical equations, at least in the directions in which the flow is spreading. This is because ...ales continue to grow as long as the flow remains turbulent. The dynamical equations and boundary conditions for many free shear flows can be shown to admit to
  67 KB (11,204 words) - 13:42, 19 April 2016
• Hydrodynamic/acoustic splitting
  ...turbed quantities denoted by ('). The original full perturbed compressible equations (PCE) ... quantities can be derived by subtracting the incompressible Navier-Stokes equations from the
  7 KB (1,056 words) - 22:26, 30 July 2008
• Riemann Problem
  ...ives an exact solution to complicated, non-linear equations like the Euler equations.
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• Solution of Boltzmann Equation
  ...scani in 2004 studied spectral methods for numerical solution of Boltzmann equations and Ibragimov, Rjasanow in 2002 proved an <math>O(n^{-2})</math> numerical Recent results that improve the numerical solution of Boltzmann equations are done in 2007 by [http://www.elegant-mathematics.com/gpu-boltzmann.pdf I
  5 KB (908 words) - 03:08, 13 May 2010
• Immersed boundary method
  ...he force of the surface of the object on the fluid) to the Navier–Stokes equations. This force density, if chosen properly, should result in a solution to the
  3 KB (451 words) - 07:08, 17 September 2009
• RANS-based turbulence models
  [[Introduction to turbulence/Reynolds averaged equations]] ...equations is to compute the [[Introduction to turbulence/Reynolds averaged equations|Reynolds stresses]], which can be done by three main categories of RANS-bas
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• Linear eddy viscosity models
  ...ulence/Reynolds averaged equations|Reynolds averaging of the Navier-Stokes equations]], are modelled by a ''linear constitutive relationship'' with the ''mean'' ...relationship, check section [[Introduction to turbulence/Reynolds averaged equations]].
  2 KB (267 words) - 18:38, 7 June 2011
• Nonlinear eddy viscosity models
  ...dels for the [[Introduction to turbulence/Reynolds averaged equations|RANS equations]] in which an [[Linear eddy viscosity models|eddy viscosity coefficient]] i
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• Sample code for solving Lid-Driven cavity test (Re=1000) - Fortran 90
  *[[Solve_UV.f90 - Solution of the momentum equations for U and V]] *[[TDMA.f90 - Solution of system of linear equations by Thomas method]]
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• TDMA.f90 - Solution of system of linear equations by Thomas method
  ! solution of linear system of equations by Thomas algorithm modul
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• Calculation on non-orthogonal curvelinear structured grids, finite-volume method
  Using the finite volume method the trnsformed equations can be integrated as follows:
  5 KB (696 words) - 10:24, 20 August 2010
• Introduction to turbulence/Wall bounded turbulent flows
  equations to satisfy this condition, and it can be met even by solutions to to the inviscid Euler’s equations.
  41 KB (7,002 words) - 13:02, 21 March 2012
• Code: Lid driven cavity using pressure free velocity form
  ...ompressible Navier-Stokes equation is composite, the sum of two orthogonal equations, ...nd from the Helmholtz Theorem, showing that these are integro-differential equations, and not particularly convenient for numerical computation.
  11 KB (1,560 words) - 20:12, 15 March 2013
• Code: Lid-driven cavity using pressure-free velocity form (2)
  ...ompressible Navier-Stokes equation is composite, the sum of two orthogonal equations, ...nd from the Helmholtz Theorem, showing that these are integro-differential equations, and not particularly convenient for numerical computation.
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• HiFlow³
  ...urate solution of a wide range of problems modeled by partial differential equations. Based on object-oriented concepts and the full capabilities of C++ the HiF
  1,010 B (136 words) - 09:04, 30 April 2012
• Code: Thermal cavity using pressure-free velocity form
  ...ompressible Navier-Stokes equation is composite, the sum of two orthogonal equations, ...nd from the Helmholtz Theorem, showing that these are integro-differential equations, and not particularly convenient for numerical computation.
  14 KB (1,998 words) - 21:21, 15 March 2013
• Code: 3D Lid-driven cavity using pressure-free velocity form
  ...ompressible Navier-Stokes equation is composite, the sum of two orthogonal equations, ...nd from the Helmholtz Theorem, showing that these are integro-differential equations, and not particularly convenient for numerical computation.
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• SIMPLER algorithm - SIMPLE - Revised
  ... and hence calculate <math>\hat{u}, \hat{v}, \hat{w} </math> from momentum equations by substituting the value of the neiboughbor velocities <math>u_{nb}</math> 7. Solve the discretization equations for other <math>\varphi</math> if necessary
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• PISO algorithm - Pressure Implicit with Split Operator
  ... PISO is a pressure-velocity calculation procedure for the [[Navier-Stokes equations]] developed originally for non-iterative computation of unsteady compressib 1. Solution of the implicitly discretized fluid flow equations by operator-splitting, Journal of Computational Physics 62 by R. Issa
  4 KB (680 words) - 11:28, 5 May 2015
• SU2
  ...ization''' in mind, but is extensible to treat arbitrary sets of governing equations such as potential flow, electrodynamics, chemically reacting flows, and man
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• What is Open Source?
  ...vers that are used to solve complicated continuous functions and governing equations are often based on trial and error experiments and shrewd guesses and an em ...is extensible (and has been extended) to treat arbitrary sets of governing equations such as electrodynamics, chemically reacting flows, and many others." ''- f
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• Courant–Friedrichs–Lewy condition
  It is an important stability criterion for hyperbolic equations.
  3 KB (526 words) - 11:58, 26 August 2012
• Basic aspects of discretization
  # Discretization of the governing equations over the mesh
  1 KB (219 words) - 04:34, 21 May 2014
• Gresho vortex
  ...ortex problem independent of time for the case of [[inviscid flow]] (Euler equations). Angular velocity <math>u_{\phi}</math> depends only on radius and the cen ...son of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations]. SIAM J. Sci. Comput., 25(3), 995–1017 (23 pages).
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• Dune
  ...rics Environment is a modular C++ toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of meth
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• CONVERGE FAQ
  solving transport equations = 3.37 seconds (86.50%) In the equations above, <math>d_0 </math> and <math> A_0 </math> are the nominal diameter an
  85 KB (13,492 words) - 15:51, 10 August 2020