Navier-Stokes solvers

- Pressure-correction method
- This is the usual method being used in most computations including multi-phase flows and liquid crystal models.

- Consistent splitting method
- For the fully discrete scheme, the accuracy and stability are already proved rigorously (cf. Shen & Yang, 2007). However, for the second-order scheme, the mathematical proof of stability are extremely hard and remain to be open questions.

- Velocity-correction method
- For the fully discrete schemes of first- and second-order, the accuracy and stability are already proved rigorously (Guermond, Shen & Yang, 2008).

- Modified first-order penalty method
- This is a new and interesting scheme as it appears to be the only unconditionally stable scheme for time-dependent Stokes equations that only needs to solve a decoupled Poisson-type equation for each of the velocity components. However, it appears difficult to design a stable, second-order version of this scheme since a higher-order extrapolation for "Curl Curl u_{n+1}" would render the scheme unstable. (Shen & Yang, 2008)

Page last modified on September 15, 2008, at 10:12 PM EST

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