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SIMPLE
- Assume Navier-Stokes equations for steady-state incompressible fluid flow
- Mass conservation equation (continuity equation)
- Momentum conservation equation (velocity equation)
- When we discretize momentum conservation equation, we get:
- Matrix linear system:
- Matrix
is diagonal, with diagonal of original matrix 
is a vector corresponding to (
)- Rewriting () with substitution from ():
- Express
from equation (), i.e. momentum correction equation : - To momentum correction equation () applying continuity equation () getting:
- SIMPLE algorithm description:
- Computation starts, initial
and 
are chosen - Time step starts
- Boundary conditions are updated
- Linear system is solved
- Relaxation
- Obtained new
- Building matrix and vector
- Mass flow over cell faces is computed
- Pressure correction is applied ()
- Relaxation
- Obtained new
- Mass flow over cell faces is corrected
- Momentum correction is applied ()
- Obtained new corrected
- Boundary conditions are updated
- Steps 5 – 15 are repeated with respect to nCorrectors value
- Time step ends
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