论文标题
通过投影方法和差异代数方法，将稳定的显式runge-kutta方法应用于不可压缩的Navier-Stokes方程
Application of Stabilized Explicit Runge-Kutta Methods to the Incompressible Navier-Stokes Equations by means of a Projection Method and a Differential Algebraic Approach
论文作者
论文摘要
在本主论文中，我们已经将不同的二阶二阶稳定性runge-kutta方法稳定在不可压缩的Navier-Stokes方程中，并通过投影方法和差分代数方法进行了比较。当与投影和差分代数方法相结合时，我们探讨了RKC，ROCK2和PIROCK方案的稳定性和准确性。 Pirock显示出意外的不稳定性，Rock2导致了考虑到最有效，最通用的runge-kutta方法。差分代数方法在计算上听起来很昂贵，但表现出更好的准确性和更大的稳定区域。这些属性使其比投影方法更有效。在第一章中提出的理论得到了数值实验的支持。
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.
