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In this master thesis we have compared different second order stabilizedexplicit Runge-Kutta methods when applied to the incompressible Navier-Stokesequations by means of a projection method and a differential algebraicapproach. We explored the stability and accuracy properties of the RKC, ROCK2and PIROCK schemes when coupled with the projection and the differentialalgebraic approach. PIROCK has shown unexpected instabilities, ROCK2 resultedto be the most efficient and versatile Runge-Kutta method taken into account.The differential algebraic approach sounds computationally costly but itexhibits better accuracy and a larger stability region. These properties makeit more efficient than the projection method. The theory presented in the firstchapters is supported by numerical experiments.

Application of Stabilized Explicit Runge-Kutta Methods to the  Incompressible Navier-Stokes Equations by means of a Projection Method and a  Differential Algebraic Approach