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

Abstract

In this master thesis we have compared different second order stabilized explicit Runge-Kutta methods when applied to the incompressible Navier-Stokes equations by means of a projection method and a differential algebraic approach. We explored the stability and accuracy properties of the RKC, ROCK2 and PIROCK schemes when coupled with the projection and the differential algebraic approach. PIROCK has shown unexpected instabilities, ROCK2 resulted to be the most efficient and versatile Runge-Kutta method taken into account. The differential algebraic approach sounds computationally costly but it exhibits better accuracy and a larger stability region. These properties make it more efficient than the projection method. The theory presented in the first chapters is supported by numerical experiments.