# SIMPLE algorithm

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- | == | + | ==SIMPLE== |

If a steady-state problem is being solved iteratively, it is not necessary to fully resolve | If a steady-state problem is being solved iteratively, it is not necessary to fully resolve | ||

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+ | ==SIMPLE Solver Algorithm == | ||

+ | The algorithm may be summarized as follows: | ||

+ | The basic steps in the solution update are as follows: | ||

+ | |||

+ | #Set the boundary conditions. | ||

+ | #Computed the gradients of velocity and pressure. | ||

+ | #Solve the discretized momentum equation to compute the intermediate velocity field . | ||

+ | #Compute the uncorrected mass fluxes at faces . | ||

+ | #Solve the pressure correction equation to produce cell values of the pressure correction . | ||

+ | #Update the pressure field: <math> p^{k + 1} = p^k + urf \bullet p^' </math> where urf is the under-relaxation factor for pressure. | ||

+ | #Update the boundary pressure corrections <math> p_b^' </math>. | ||

+ | #Correct the face mass fluxes: <math>\dot m_f^{k + 1} = \dot m_f^* + \dot m_f^' </math> | ||

+ | #Correct the cell velocities: <math> \vec v^{k + 1} = \vec v^* - \frac{{Vol\nabla p^' }}{{\vec a_P^v }} </math> ; where <math> {\nabla p^' } </math> is the gradient of the pressure corrections, <math> {\vec a_P^v } </math> is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume. | ||

+ | #Update density due to pressure changes. | ||

+ | |||

+ | |||

---- | ---- | ||

<i> Return to [[Numerical methods | Numerical Methods]] </i> | <i> Return to [[Numerical methods | Numerical Methods]] </i> |

## Revision as of 10:27, 23 October 2005

## SIMPLE

If a steady-state problem is being solved iteratively, it is not necessary to fully resolve the linear pressure-velocity coupling, as the changes between consecutive solutions are no longer small. The SIMPLE algorithm:

- An approximation of the velocity field is obtained by solving the momentum equation. The pressure gradient term is calculated using the pressure distribution from the previous iteration or an initial guess.
- The pressure equation is formulated and solved in order to obtain the new pressure distribution.
- Velocities are corrected and a new set of conservative fluxes is calculated.

## SIMPLE Solver Algorithm

The algorithm may be summarized as follows:

The basic steps in the solution update are as follows:

- Set the boundary conditions.
- Computed the gradients of velocity and pressure.
- Solve the discretized momentum equation to compute the intermediate velocity field .
- Compute the uncorrected mass fluxes at faces .
- Solve the pressure correction equation to produce cell values of the pressure correction .
- Update the pressure field: where urf is the under-relaxation factor for pressure.
- Update the boundary pressure corrections .
- Correct the face mass fluxes:
- Correct the cell velocities: ; where is the gradient of the pressure corrections, is the vector of central coefficients for the discretized linear system representing the velocity equation and Vol is the cell volume.
- Update density due to pressure changes.

* Return to Numerical Methods *