Time‐adaptive multirate generalized‐structure additively partitioned Runge‐Kutta schemes for mechanical fluid‐structure interaction

Abstract

We extend the multirate GARK approach by Günther and Sandu [1, 2] to the case of non‐constant micro steps per macro step to be able to cover time adaptivity, arriving at our so‐called TAMGARK scheme and derive order conditions for arbitrary non‐constant micro step sizes. The TAMGARK scheme is applied to the classical piston problem [3] to study the interaction between the piston and inviscid fluid flow in one spatial dimension. We demonstrate the functionality of the chosen time‐adaptation strategy and the ability of the overall scheme to preserve the order of the basic schemes. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)