Search results

Create the page "Equations" on this wiki!

• 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