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Solution of Navier-Stokes equations

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# Non linearity of momentum equations
# Non linearity of momentum equations
# Pressure-velocity coupling
# Pressure-velocity coupling
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==Segregated Solver==
==Segregated Solver==
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=== The solution scheme ===
=== The solution scheme ===
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## Correct fluxes and velocities
## Correct fluxes and velocities
# Solve transport equations for other scalars
# Solve transport equations for other scalars
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== Coupled Solver ==
== Coupled Solver ==

Revision as of 23:08, 20 December 2005

For the incompressible flows, the Navier-Stokes equation could be written in the form:


\nabla  \cdot \vec U = 0
 {{\partial \vec U} \over {\partial t}} + \nabla  \cdot \left( {\vec U\vec U} \right) -  \nabla  \cdot\left( {\nu \nabla \vec U} \right) =  - \nabla p

There are two important issues regarding Navier-Stokes equations:

  1. Non linearity of momentum equations
  2. Pressure-velocity coupling

Segregated Solver

The solution scheme

  1. Solve Momentum equations (u,v,w)
  2. Solve pressure correction equation
    1. Correct fluxes and velocities
  3. Solve transport equations for other scalars

Coupled Solver

  1. Solve the Momentum equations- Pressure equation system in one go (u,v,w,p)
  2. Solve transport equations for other scalars

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