Automatic step size selection for the fractional-step-theta-scheme

by Rang, J.


Preprint series: 06-45, Preprints

76D05 Navier-Stokes equations, See also {35Q30}
35Q30 Stokes and Navier-Stokes equations, See also {76D05, 76D07, 76N10}
65L20 Stability of numerical methods
65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods


Abstract: In this note the fractional-step-$\theta$-scheme is written as a diagonally implicit Runge-Kutta method (DIRK method). In this context a strongly A-stable embedded formula of order one is created such that an ODE or a DAE can be solved with automatic step length control. Moreover the implementation of Runge-Kutta methods applied on DAEs of index 2 is explained. Finally, we apply the new method with automatic step size control on the incompressible Navier-Stokes equations. The numerical results show the advantage of the method.

Keywords: imcompressible Navier-Stokes equations, implicit $\theta$-schemes, Runge-Kutta-methods, order reduction

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Letzte Änderung: 01.03.2018 - Ansprechpartner: Webmaster