SIMPLE algorithm: Difference between revisions

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== Algorithm ==
The algorithm is [[iterative]]. The basic steps in the solution update are as follows:
 
#Set the boundary conditions.
#Compute 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.