pressurecorrection

Pressure correction is a technique used in computational fluid dynamics (CFD) to handle the interdependence between velocity and pressure fields, particularly in incompressible flow problems. In the Navier-Stokes equations, pressure does not have its own explicit transport equation. Instead, it acts as a Lagrange multiplier to enforce the incompressibility constraint, meaning the divergence of the velocity field must be zero.

Directly solving the primitive variables (velocity and pressure) simultaneously can be challenging. Pressure correction methods iteratively adjust the pressure field to ensure that the resulting velocity field satisfies the continuity equation. Common algorithms include the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) family of methods, which involve a predictor-corrector approach.

In the predictor step, a provisional velocity field is computed using the current pressure estimate. This provisional velocity field generally does not satisfy continuity. In the corrector step, a pressure correction equation is derived. This equation relates the pressure correction to the imbalance in the continuity equation. By solving this pressure correction equation, an updated pressure field is obtained, which is then used to correct the provisional velocity field. This process is repeated until both the momentum and continuity equations are satisfied to a desired level of accuracy. Pressure correction is a fundamental concept for solving a wide range of fluid flow problems.